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Mathematics Questions and Answers January 13, 2018

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( 2 . 6 ) Let f ( x ) = - 2 x 2 + 3 x + 1 . Find the average rate of change of f as x ranges from a to a + h .
( 2 . 6 ) Let f ( x ) = - 2 x 2 + 3 x + 1 . Find

Evaluate the indefinite integral. l n ( c o s - 1 ( x ) ) d x 1 0 ( c o s - 1 ( x ) ) 1 - x 2 2 ( Express numbers in exact form. Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C as much as possible. ) l n ( c o s - 1 ( x ) ) d x 1 0 ( c o s - 1 ( x ) ) 1 - x 2 2 =
Evaluate the indefinite integral. l n ( c o s - 1

A music album by a popular artist goes on sale at time t = 0 . The total number of albums sold t hours after the sale begins is modeled by the function A , where A is measured in hundreds of albums and 0 = t = 2 4 . If A satisfies the differential equation ( dA ) / ( dt ) = ( 3 t + 7 ) / ( A ) with A ( 1 ) = 5 , find an equation for A ( t ) .
A music album by a popular artist goes on sale at

Suppose a change of coordinates T : R 2 R 2 from the u v - plane to the x y - plane is given by x = v + 4 u + 1 , y = 4 - 5 u + v ( a ) Find the absolute value of the determinant of the Jacobian for this change of coordinates. | d e l ( x , y ) d e l ( u , v ) | = | d e t [ - ] + | | = ( b ) If a region D * * in the u v - plane has area 7 . 3 6 ,
Suppose a change of coordinates T : R 2 R 2 from

Help Entering Answers ( 1 point ) Use the Divergence Theorem to calculate the outward flux of F = r | r | where r = ( : x , y , z : ) across S : the hemisphere z = 1 - x 2 - y 2 2 and the disk x 2 + y 2 1 in the x y - plane. Flux of F across S = x 1 x 2 y 1 y 2 z 1 z 2 d z d y d x where x 1 = , , y 1 = x 2 = , , y 2 = z 1 = z 2 = Flux of F across
Help Entering Answers ( 1 point ) Use the

Use ( i ) the Fundamental Theorem of calc. a b f ( x ) d x = F ( b ) - F ( a ) , where f ' ( x ) = f ( x ) , and ( ib ) limits to evaluate: 1 1 x 7 d x =

Differentiate the following function. Bold r left parenthesis t right parenthesis equalsleft angle 6 t Superscript 4 Baseline comma 6 StartRoot t EndRoot comma StartFraction 9 Over t EndFraction right angle

Find the derivative. y ( x ) = x sinh 1 x 4 1 6 + x 2

Talk about the stability of stationary states for the equation dx / dt = x ( 4 - x ^ 2 )

Evaluate the definite integral. 1 6 x 1 6 + 3 x dx 0 1 9

Consider the following function and closed interval. f ( x ) = ( x - 2 ) ( x - 4 ) ( x - 7 ) , [ 2 , 7 ] Is f continuous on the closed interval [ 2 , 7 ] ? Yes No If f is differentiable on the open interval ( 2 , 7 ) , find f ' ( x ) . ( If it is not differentiable on the open interval, enter DNE. ) f ' ( x ) = Find f ( 2 ) and f ( 7 ) . f ( 2 ) =
Consider the following function and closed

integral 0 - 1 3 / ( x ^ 2 - 2 x + 1 )

Find the derivative of the function: u ( x ) = ( x ^ 2 + 1 ) ^ 4 x 2 1

Find the area of the shaded region enclosed by the following functions. Set up the integral that gives the area of the shaded region. Select the correct choice below, and fill in the answer boxes within your choice. A . - 1 7 | d y + 0 | d y + 1 5 | d y | | B . - 1 7 1 d y C . - 8 d x + - 7 d x + 8 d x D .
Find the area of the shaded region enclosed by

How many grams of sodium are present in a sample containing 3 . 7 2 x 1 0 2 4 atoms of sodium?

Theorem 7 . 2 . 1 - Some Inverse Transforms a . 1 = L ^ ( - 1 ) { ( 1 ) / ( s ) } b . t ^ ( n ) = L ^ ( - 1 ) { ( n ! ) / ( s ^ ( n + 1 ) ) } , n = 1 , 2 , 3 , dots c . e ^ ( at ) = L ^ ( - 1 ) { ( 1 ) / ( s - a ) } d . sin ( kt ) = L ^ ( - 1 ) { ( k ) / ( s ^ ( 2 ) + k ^ ( 2 ) ) } e . cos ( kt ) = L ^ ( - 1 ) { ( s ) / ( s ^ ( 2 ) + k ^ ( 2 ) ) }
Theorem 7 . 2 . 1 - Some Inverse Transforms a . 1

( no calculator ) \ table [ [ x , f ( x ) , f ' ( x )
( no calculator ) \ table [ [ x , f ( x ) , f ' (

lim x - > e ^ 2 ^ / x ^ 3

4 e ( - 2 x ) * e ( - 0 . 1 x 3 3 0 ) fid du / dx

Automatic Zoom ( a ) Evaluate the following limits: ( i ) lim x 0 a r c s i n ( 2 x + x 2 ) l n ( 1 + 3 x ) [ 4 marks ] ( ii ) lim x 0 + ( s i n x ) x [ 4 marks ]

In the following exercises, find the average value of between and , and find a point / points , where ( ) = . When calculating the integral, you can use area or the definite integral formula. 1 1 3 . ( ) = 3 | | , = 3 , = 3 1 1 4 . ( ) = sin , = 0 , = 2
In the following exercises, find the average

If the demand for an item is given by the function 8 p + 2 0 q = 1 2 0 0 and the supply function is given by 2 p - 4 q = 4 0 where p is the price and q is the quantity of units, compare the supply and demand when the price is $ 9 0 . ( a ) ( 5 Points ) Determine the quantity demanded when the price is $ 9 0 ( b ) ( 5 Points ) Determine the

Q # 7 ( 4 pts ) The velocity of an object is found to be v ( t ) = 8 t 2 + 5 t - 3 meters per seeond at time t seconds. If at time t = 1 the object is located at position s ( 1 ) = 2 meters, find the position of the object at time t = 4 seconds.
Q # 7 ( 4 pts ) The velocity of an object is

C to represent a constant. \ int ( 5 e ^ ( x ) + 1 2 sin ( x ) ) dx =
C to represent a constant. \ int ( 5 e ^ ( x ) +

H . w t 2 y ' ' - 2 y = t 3 given that y 1 ( t ) = 1 t is the solution of the honogerous equation H . w t 2 y ' ' - 2 y = t 3 given that y 1 ( t ) = 1 t is the solution of the honogerous equation H . w t 2 y ' ' - 2 y = t 3
H . w t 2 y ' ' - 2 y = t 3 given that y 1 ( t )

Evaluate the indefinite integral. 2 x - 2 ( 2 x 2 - 4 x + 1 ) 6 d x
Evaluate the indefinite integral. 2 x - 2 ( 2 x 2

What is the area of the largest rectangle that can fit in the region above the x - axis and below the curve y = 2 1 + 4 x 2 ?
What is the area of the largest rectangle that

Do the same for these IVPs. ( a ) x 2 d u d x - ( u 2 + x u ) = 0 , u ( 1 ) = 1 . ( b ) ( u + x ) d u d x + u + 2 x 3 = 0 , u ( 0 ) = 1 . The quadratic formula may help on part ( b ) .
Do the same for these IVPs. ( a ) x 2 d u d x - (

Find Z 5 0 f ( x ) dx if f ( x ) = 3 for x < 3 , x for x 3 .

Let g ( t ) = 6 t 2 + 4 . ( a ) Find g ' ( 3 ) . ( b ) Find g ' ( a )

You're building a box with square top and bottom. The material for the sides of the box costs $ 5 per square meter and the material for the top and bottom costs $ 7 per square meter. The box needs to enclose a volume of 1 0 0 cubic meters. What is the minimal cost of a box you can build with these constraints? Enter your answer as a decimal within
You're building a box with square top and bottom.

c ( x + 2 ) d s where C is the curve represented by r ( t ) = t 1 + 4 3 t 3 2 j + 1 2 t 2 k for 0 t 2
c ( x + 2 ) d s where C is the curve represented

What is the slope of the line that passes through the points ( 2 , - 4 ) and ( 8 , 0 )

Q 6 Determine whether the following series is convergent or Divergent by using the Limit Comparison Test. Make sure to state the serics ? ? b n , that you are comparing to , & why the series ? ? b n is convergent or divergent n = 1 n 2 - 1 n 4 + 5
Q 6 Determine whether the following series is

x 2 ( 4 - x 2 2 2 ) dx using u sub and dv

Find the derivative of the function f ( x ) = ln ( 2 x ^ 4 + x ^ 2 3 )

Find the Left and Right Riemann Sums for the following function on the interval 1 , 5 using 4 subintervals. If necessary, round your final answers to two decimal places. f ( x ) = 1 3 x 2 + x + 2 6 Left Riemann Sum = Right Riemann Sum =
Find the Left and Right Riemann Sums for the

Let \ [ h ( x ) = \ sqrt { \ sin ( x ) } \ ] . Find \ [ h ' ( x ) \ ] .

1 . Use Newton s method starting with x = - 1 to find x 3 the third approximation of the root of x 7 + 4 = 0 2 . Use Newton s method to approximate 1 0 0 1 0 0 to 4 decimal places.

Calculate x 2 z d S , where is the cylinder ( including the top and bottom ) x 2 + y 2 = 4 , 0 z 4 . ( Use symbolic notation and fractions where needed. ) x 2 z d S = Incorrect Answer
Calculate x 2 z d S , where is the cylinder (

Evaluate the indefinite integrals. ( a ) sin 3 ( 5 x ) cos ( 5 x ) dx = + C .

Question 1 1 0 / 4 pts 0 3 Details Find x e 3 x d x C Calculator
Question 1 1 0 / 4 pts 0 3 Details Find x e 3 x d

Evaluate the indefinite integral ( x ^ 2 - x + 1 ) / ( x ^ 4 - x ^ 2 )

y = x + 9 1 4 x ^ ( 2 ) + y ^ ( 2 ) = 8 1 List all the solutions. Select the correct choice and, if necess

( 6 points ) Consider the following function f ( x ) = 1 + x 2 3 1 x - 1 = 3 e 1 + x 2 = > 3 e x 2 Find the Taylor polynomial T 2 ( x ) o f degree 2 near x = 0 o f f ( x ) . f ( a ) = 3 2 ( 1 + x ) 1 2 = x n , x 2 = f ( 0 ) + f ( 0 ) ' 1 ! x - a + f ' ' ( 0 ) 2 ! ( x - a ) 2 + f ' ' ' ( c ) 3 ! f ' ( 0 ) = 1 e 2 a = ( 3 2 ) ( 1 2 ) ( 1 + x ) = Z (
( 6 points ) Consider the following function f (

Find the x - intercept ( s ) and the coordinates of the vertex for the parabola y = - x ^ ( 2 ) + 8 x - 7 .

( 1 point ) Evaluate the indefinite integral. 8 t + 9 2 d t = + C .
( 1 point ) Evaluate the indefinite integral. 8 t

Are the following series absolutely convergent, conditionally convergent or divergent? ( use the appropriate test ) . n = 1 n 2 r 3 + 1 . n = 1 ( - 5 ) 2 n n 2 9 n . n = 0 n n 4 n n ! . n = 1 n e - n . 5 . 4 - 1 + 1 4 - 1 1 6 + 1 6 4 - dots n = 1 1 n n 2 + 1 2 . n = 0 1 ( 2 n + 1 ) ! . n = 1 1 n ( 1 + l n 2 n ) n = 1 1 * 3 * 5 * c d o t s * ( 2 n
Are the following series absolutely convergent,

Evaluate the definite integral: \ int _ 0 ^ ( \ sqrt ( 3 ) ) ( x ) / ( \ sqrt ( 4 - x ^ ( 2 ) ) ) dx . ( \ pi ) / ( 3 ) 2 1 - 1 ( \ pi ) / ( 6 )
Evaluate the definite integral: \ int _ 0 ^ ( \

Find f ' ( a ) . f ( t ) = 6 t + 4 t + 8 To find f ' ( a ) , we will use the formula f ' ( a ) = lim t a f ( t ) - f ( a ) t - a Since f ( t ) = 6 t + 4 t + 8 we have f ' ( a ) = lim t a 6 t + 4 t + 8 - 6 a + 4 a + 8 t - a Simplifying everything we get f ' ( a ) = lim t a | | | = Find f ' ( a ) . f ( t ) = 6 t + 4 t + 8 To find f ' ( a ) , we will
Find f ' ( a ) . f ( t ) = 6 t + 4 t + 8 To find

Let R = { ( x , y ) | 0 x 4 , x 2 y 2 } . a . Sketch and shade region R on the x y - plane. b . Evaluate the integral R 1 y 3 + 1 d A .
Let R = { ( x , y ) | 0 x 4 , x 2 y 2 } . a .

1 . An animal population is increasing at a rate of 1 5 + 5 1 t per year ( where t is measured in years ) . By how much does the animal population increase between the fourth and tenth years?

a sequence is defined by f ( 1 ) = 4 , f ( n ) = f ( n - 1 ) - 5 . write a closed form definition for this sequence.

code class = "asciimath" > Implement the Hill Climbing algorithm to solve the following problem: Find the values of x 1 and x 2 that satisfy the equation: x 1 2 + x 2 2 = 1 0 0 The evaluation function is defined as: x 1 2 + x 2 2 - 1 0 0 = 0

The function z 2 + 1 is even.

Solve the inequality for v . - 1 8 < = - 8 - ( 5 ) / ( 3 ) v Simplify your answer as much as possible.

\ table [ [ t ( min ) , 5 , 1 0 , 1 5 , 2 0 , 2 5 , 3 0 ] , [ v ( gal ) , 2 , 0 5 8 , 1 , 2 9 6 , 7 6 5 , 3 4 2 , 8 1 , 0 ] ] \ table [ [ Q , Slope ] , [ ( 5 , 2 , 0 5 8 ) , ] , [ ( 1 0 , 1 , 2 9 6 ) , ] , [ ( 2 0 , 3 4 2 ) , ] , [ ( 2 5 , 8 1 ) , ] , [ ( 3 0 , 0 ) , ] ]
\ table [ [ t ( min ) , 5 , 1 0 , 1 5 , 2 0 , 2 5

The place you work at is organizing a 2 days event. You are selected to lead the promotion team where you have to prepare different size of posters. These posters must be ready a month before the actual event take place. Among the different size of posters, you are in charge of designing a special rectangular poster that contain 5 0 \ ( \ mathrm {
The place you work at is organizing a 2 days

[ - / 1 . 0 6 Points ] SCALCET 9 Express the function as the sum of a power series by first using par Find the interval of convergence. ( Enter your answer using interval
[ - / 1 . 0 6 Points ] SCALCET 9 Express the

Two chemicals A and B are combined to form a Chemical C . The rate of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C . Initially there are 3 5 grams of A and 5 0 grams of B , and for each gram of A , 2 grams of B is used. It is observed that 1 0 grams of C is formed in 5 minutes. a .
Two chemicals A and B are combined to form a

Find the indefinite integral. ( a ) 1 x l n x 3 d x ( b ) e - x t a n e - x d x ( c ) 1 x 2 - 1 d x ( d ) x x - 1 2 d x ( e ) 1 x 2 2 5 - x 2 2 d x ( f ) ( 1 + c o s ) 2 d ( g ) x 2 l n x d x ( h ) ( l n x ) 2 d x ( i ) 5 x - 3 x 2 - 2 x - 3 d x
Find the indefinite integral. ( a ) 1 x l n x 3 d

Evaluate the integral. 2 4 y 2 6 y 1 2 y ( y + 2 ) ( y 3 ) dy 1 ln ( 8 3 )

derivative of composite functions f ( x ) = ( x + 3 ) ^ 2

Find the limit . lim t 0 e 7 t i + t 2 sin 2 ( t ) j + tan ( 5 t ) k

Find dydx by implicit differentiation, where 6 x 3 + x 2 y 7 xy 3 = 5 .

Select the equation for the line crossing the points ( - 3 , 5 ) and ( 1 , 3 )

Evaluate the limit of 1 - cos x over x ^ 2 times e ^ 2 as x approaches 0

Use the Integral Test to determine whether the series is convergent or divergent. n = 1 4 9 n 1 Evaluate the following integral. 1 4 9 x 1 dx

Question What is the difference barwocn 2 8 . 9 3 5 and 1 3 . 0 1 1 , to the nearest integer?

\ int _ { 1 } ^ { \ infty } \ frac { 1 } { x ^ { 6 } } \ , dx

Let f ( x ) = 3 x 2 5 x + 3 f ( x ) = 3 x 2 5 x + 3 . Compute f ( 3 ) . Answer: Use this to find the equation of the tangent line to the parabola y = 3 x ^ 2 5 x + 3 at the point ( 3 , 4 5 ) . The equation of this tangent line can be written in the form y = mx + b . Determine m and b .

Use the zero - factor property to solve the equation. 7 x ^ ( 2 ) = 3 9 x - 2 0

In 1 9 6 0 , the world record for the men's mile was 3 . 9 1 minutes. In 1 9 8 0 , the record time was 3 . 8 1 minutes. a . Write a linear model that represents the world record ( in minutes ) for the men's mile as a function of the number of years, t , since 1 9 6 0 . y

derivative y = ( \ sqrt ( 1 - x ^ ( 2 ) ) ) / ( x )

6 e ^ 6 x * sin ( e ^ 6 x ) dx

4 . Find the value of to 1 0 decimal places by using any of the methods we have covered to find the first positive root of the sine function

Find an equation of the tangent line to the curve at the given point. y = 3 x 2 6 x + 1 , ( 3 , 1 0 ) y =

Find the inverse Laplace transform, f ( t ) of the function F ( s ) = ( s ) / ( ( s - 2 ) ( s + 9 ) ( s - 5 ) ) * s > f ( t ) = , t > 0
Find the inverse Laplace transform, f ( t ) of

1 5 . The population of ndonesia from 1 9 5 0 to 2 0 0 0 has been modeled with the function Pstd 8 3 e 0 . 1 8 t where P is measured in millions and t is measured in years with t 0 in the year 1 9 5 0 . What was the average population of Indonesia in the second half of the 2 0 th century?

Evaluate the definite integral. ln ( 3 ) 1 0 e x cosh ( x ) dx 0

For the three points ( 1 , 7 ) , ( 2 , 6 ) and ( - 1 , 1 8 ) , find a quadratic model y = ax ^ 2 + bx + c through the points. Round your answers to one decimal as needed.

Finding the slope of a line given its equatio Find the slope of the line. y = 4 Write your answer in simplest form.

Solving a system of nonlinear equations: Problem type 1 Solve the following system of equations. y + 5 x = 2 1 5 x ^ ( 2 ) - 4 x - y = 4 If there is more than one solution, enter additional solu If there is no real solution, use the " No solution" button

Calculate the integral approximation S 1 0 for 4 9 x 1 6 d x . S 1 0 =
Calculate the integral approximation S 1 0 for 4

Evaluare the definite integral exactly using the fundamental theorum - 5 - 1 4 r 5 dr

H = acos ( bt ) + c Find Tom's height above the ground when a = - 1 5 m , b = 2 . 4 1 ra ( d ) / ( s ) , t = 3 s , and c = 2 3 m .

Fill in the missing values in the table given that d y d t = 0 . 5 y . Assume the rate of growth given by d y d t is approximately constant over each unit time interval and that the initial value of y is 4 . Enter the exact answers. \ table [ [ t , 0 , 1 , 2 , 3 , 4 ] , [ y , 4 , i , , , ] , [ , , , , , ] ]
Fill in the missing values in the table given

Suppose you plan to have $ 7 0 , 0 0 0 in 1 0 years from now and you can invest your savings at 7 % compounded continuously. Assuming you can save the same amount of money each year, how much do you need to save on a yearly basis in order to achieve your goal? Hint: Treat your savings as an income stream. Yearly savings ( exact value ) = dollars

Problem 4 . Draw ( qualitatively ) the integral curves of the ODE: y ' = x + 4 y x - y
Problem 4 . Draw ( qualitatively ) the integral

Find the arc length of the curve x = - 4 y 3 2 from y = 0 to y = 7 . Length =
Find the arc length of the curve x = - 4 y 3 2

code class = "asciimath" > A water wave traveling in a straight line on a lake is described by the equation y ( x , t ) = ( 2 . 7 5 cm ) cos ( 0 . 4 1 0 ra ( d ) / ( c ) mx + 6 . 2 0 ra ( d ) / ( s ) t ) where y is the displacement perpendicular to the undisturbed surface of the lake.
code class = "asciimath" style="width: 25%; display: block; margin-left: 0; margin-right: auto;"></a></div> </h2> </div> </div> <div class="related-question-statment col-md-12 col-lg-12"> <div class="no-padding question-statement-complete-placement"> <h2 class="small_h2"> <a href="/study-help/questions/1-point-it-can-be-shown-that-the-27199774" class="related-question-statement-styling">( 1 point ) It can be shown that the polar curve r = asin ( ) + bcos ( ) , where a b 0 , is a circle. Find the center ( in Cartesian coordinates ) and radius of this circle in terms of a and b . Hint: Multiply both sides of the equation by r and convert to rectangular coordinates. x - coordinate of center: y - coordinate of center: Radius:</a><div class="questionHolder"><a href="/study-help/questions/1-point-it-can-be-shown-that-the-27199774"><img src="https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2025/02/67a35421832e7_15267a35420b89f5.jpg" alt="( 1 point ) It can be shown that the polar curve" class="sc-sj7gtn-1 fkZXya" style="width: 25%; display: block; margin-left: 0; margin-right: auto;"></a></div> </h2> </div> </div> <div class="related-question-statment col-md-12 col-lg-12"> <div class="no-padding question-statement-complete-placement"> <h2 class="small_h2"> <a href="/study-help/questions/use-the-graph-to-find-the-following-choose-the-correct-27199775" class="related-question-statement-styling">Use the graph to find the following. Choose the correct domain. A . x f ( x ) = 2 O ?</a><div class="questionHolder"><a href="/study-help/questions/use-the-graph-to-find-the-following-choose-the-correct-27199775"><img src="https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2025/02/67a35421a70d8_15267a35420bc961.jpg" alt="Use the graph to find the following. Choose the" class="sc-sj7gtn-1 fkZXya" style="width: 25%; display: block; margin-left: 0; margin-right: auto;"></a></div> </h2> </div> </div> <div class="related-question-statment col-md-12 col-lg-12"> <div class="no-padding question-statement-complete-placement"> <h2 class="small_h2"> <a href="/study-help/questions/a-estimate-2-8-x-2-1-27199776" class="related-question-statement-styling">( a ) Estimate 2 8 x 2 + 1 d x using n = 3 rectangles and left endpoints. Sketch a graph with and illustration of the estimate. Is the estimate bigger or smaller than the actual value. ( b ) Use the Fundamental Theorem of Calculus to find the exact value 2 8 x 2 + 1 d x . Compare with what you got above.</a><div class="questionHolder"><a href="/study-help/questions/a-estimate-2-8-x-2-1-27199776"><img src="https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2025/02/67a35421a0b9a_15267a35420c693f.jpg" alt="( a ) Estimate 2 8 x 2 + 1 d x using n = 3" class="sc-sj7gtn-1 fkZXya" style="width: 25%; display: block; margin-left: 0; margin-right: auto;"></a></div> </h2> </div> </div> <div class="related-question-statment col-md-12 col-lg-12"> <div class="no-padding question-statement-complete-placement"> <h2 class="small_h2"> <a href="/study-help/questions/d-2-y-d-t-2-4-t-d-27199777" class="related-question-statement-styling">d 2 y d t 2 - 4 t d y d t + 8 y = 4 t + 1 ; , y ( 0 ) = 3 , y ( 1 0 ) = 9 diferansiyel denkleminin say sal z mlemesi matris y ntemi kullan larak yap lmak istenmektedir. t = 1 ad m aral i in gerekli olan matrisleri yaz n z ( 2 5 puan ) .</a><div class="questionHolder"><a href="/study-help/questions/d-2-y-d-t-2-4-t-d-27199777"><img src="https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2025/02/67a35421eac75_15367a3542181036.jpg" alt="d 2 y d t 2 - 4 t d y d t + 8 y = 4 t + 1 ; , y (" class="sc-sj7gtn-1 fkZXya" style="width: 25%; display: block; margin-left: 0; margin-right: auto;"></a></div> </h2> </div> </div> <div class="related-question-statment col-md-12 col-lg-12"> <div class="no-padding question-statement-complete-placement"> <h2 class="small_h2"> <a href="/study-help/questions/find-an-equation-of-the-tangent-line-to-the-graph-27199778" class="related-question-statement-styling">Find an equation of the tangent line to the graph of y = 6 x x 2 + 1 at the origin and at the point ( - 1 , - 3 ) . The tangent to the curve at the origin is y = The tangent to the curve at the point ( - 1 , - 3 ) is y = ( Simplify your answer. )</a><div class="questionHolder"><a href="/study-help/questions/find-an-equation-of-the-tangent-line-to-the-graph-27199778"><img src="https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2025/02/67a35421e1ee2_15367a354211c551.jpg" alt="Find an equation of the tangent line to the graph" class="sc-sj7gtn-1 fkZXya" style="width: 25%; display: block; margin-left: 0; margin-right: auto;"></a></div> </h2> </div> </div> <div class="related-question-statment col-md-12 col-lg-12"> <div class="no-padding question-statement-complete-placement"> <h2 class="small_h2"> <a href="/study-help/questions/during-a-series-of-plays-in-a-football-game-a-27199779" class="related-question-statement-styling">During a series of plays in a football game, a running back carried the ball for the yardages given by 6 6 , negative 4 4 , 2 2 , negative 1 1 , 7 7 , negative 3 3 , and negative 2 2 . Find his total yards and his average yards per carry.</a> </h2> </div> </div> <div class="related-question-statment col-md-12 col-lg-12"> <div class="no-padding question-statement-complete-placement"> <h2 class="small_h2"> <a href="/study-help/questions/find-the-general-indefinite-integral-use-c-for-the-27199780" class="related-question-statement-styling">Find the general indefinite integral. ( Use C for the constant of integration. ) ( u + 6 ) ( 2 u + 5 ) du</a> </h2> </div> </div> <div class="related-question-statment col-md-12 col-lg-12"> <div class="no-padding question-statement-complete-placement"> <h2 class="small_h2"> <a href="/study-help/questions/use-a-maclaurin-series-in-the-table-below-to-obtain-27199781" class="related-question-statement-styling">Use a Maclaurin series in the table below to obtain the Maclaurin series for the given function. n = 0 f ( x ) = 6 e x + e 2 x , , 1 1 - x = n = 0 x n = 1 + x + x 2 + x 3 + cdots e x = n = 0 x n n ! = 1 + x 1 ! + x 2 2 ! + x 3 3 ! + cdots, R = 1 s i n x = n = 0 ( - 1 ) n x 2 n + 1 ( 2 n + 1 ) ! = x - x 3 3 ! + x 5 5 ! - x 7 7 ! + cdots, R = c o s</a><div class="questionHolder"><a href="/study-help/questions/use-a-maclaurin-series-in-the-table-below-to-obtain-27199781"><img src="https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2025/02/67a354220c16c_15367a35421877d8.jpg" alt="Use a Maclaurin series in the table below to" class="sc-sj7gtn-1 fkZXya" style="width: 25%; 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