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Mathematics Questions and Answers May 9, 2018

Expert-verified solutions to help you succeed

Find the second derivative of y = e ^ x ^ 3 + 7 x

find the general solution 2 . dy dt = 4 y + 3 e t

lim x 3 1 ( 2 x 6 ) 3

Solving for a variable in terms of other variab Solve for r . K = 9 r - s r

Evaluate 1 x 2 x 2 + 1 6 2 d x Enter c or C as the constant of integration.

Find the limit . ( If the limit is infinite, enter ' ' or ' - ' , as appropriate. If the limit does not otherwise exist, enter DNE. ) lim x ( / 2 ) + 5 tan ( x )

Evaluate the integral. 2 sec 6 t dt

Evaluate the following indefinite integrals. ( b ) 1 / ( y ( 2 - y ) ) dy

Let r ( t ) = 4 3 t + 3 , 7 t 4 t 2 + 7 , 5 t 2 3 t 3 + 4 r ( t ) = - 4 - 3 t + 3 , - 7 t - 4 t 2 + 7 , - 5 t 2 3 t 3 + 4 Find r ' ( t ) r ( t )

Differentiate. y equals 3 x plus left parenthesis 2 x plus 7 right parenthesis Superscript 4 y = 3 x + ( 2 x + 7 ) 4

use implicit differentiation to show that, whenever a hyperbola with equation x ^ 2 - y ^ 2 = k intersects with a hyperbola with equation xy = C , the tangent line at the points are perpendicular.

Complex conjugate of i * e ^ ( ix )

Knowing that y = 5 x + b is a linear equation and that it passes through point ( 1 , - 1 ) , determine

Find the area of the polar region f ( ) = 5 e / 2 for 0 5 / 4 . Area = ?

( a ) Which ring has more wood in it ? The napkin ring created by drilling a hole with the larger radius has more wood in it . The napkin ring created by drilling a hole with the smaller radius has more wood in it . The amount of wood in each napkin ring is the same regardless of the size of the sphere used. ( b ) Use cylindrical shells to compute
( a ) Which ring has more wood in it ? The napkin

Evaluate the following limits . If needed, enter @ 0 for and oo for - . ( a ) lim x 7 + 5 x 2 2 3 + 2 x = ( b ) lim x - 7 + 5 x 2 2 3 + 2 x =
Evaluate the following limits . If needed, enter

Find the area of the parallelogram whose vertices are given below. A ( 0 , 0 , 0 ) , B ( 3 , 4 , 5 ) , C ( 7 , 3 , 5 ) , D ( 4 , - 1 , 0 )
Find the area of the parallelogram whose vertices

Use Euler's method with step size h = 0 . 1 to approximate the solution to the initial value problem y ' = 3 x - y 2 , y ( 6 ) = 0 , at the points x = 6 . 1 , 6 . 2 , 6 . 3 , 6 . 4 , and 6 . 5 .
Use Euler's method with step size h = 0 . 1 to

For the below power series, determine the value of the interval and radius, justify that the series is convergence. n = 0 1 ( - 3 ) 2 + n ( n 2 + 1 ) ( 4 x - 1 2 ) n ( 6 Marks ) [ Total: 6 Marks ]
For the below power series, determine the value

Let g ( x ) = 0 x f ( t ) d t , for x in the interval 0 , 7 and where f is the function whose graph is shown below: ( a ) Evaluate g ( x ) for x = 0 , 1 ,
Let g ( x ) = 0 x f ( t ) d t , for x in the

( a ) Decompose the following function into partial fractions. Your answer should be written as the sum and / or difference of the fractions, including the values of A , B , and C . 1 8 y y 3 - y 2 y - 1 = ( b ) Use your answer in part ( a ) to evaluate the following integral. Remember to use absolute values where appropriate. Use C for the
( a ) Decompose the following function into

Find the first six terms of the recursive sequence. a 1 = 3 an + 1 = sqrt ( 3 ( An ) )

if a certain item has many substitues, its demand curve will be

Let f ( x ) = 5 s i n x 4 s i n x + 2 c o s x f ( x ) = 5 s i n x 4 s i n x + 2 c o s x . Then f ' ( x ) = f ' ( x ) = 1 0 ( 4 s i n x + 2 c o s x ) 2 . The equation of the tangent line to y = f ( x ) y = f ( x ) at a = 6 a = 6 can be written in the form y = m x + b y = m x + b where m = m = and b = b =
Let f ( x ) = 5 s i n x 4 s i n x + 2 c o s x f (

consider the polynomial function f ( x ) = x ^ ( 3 ) - 2 x ^ ( 2 ) - kx + 1 8 and find the value of k so that x - 9 is a factor of f

( 4 points ) Evaluate the following limit . ( Hint: Plug in x - values close to - 4 and see where it is headed ) lim x - 4 + x + 2 x + 4
( 4 points ) Evaluate the following limit . (

Repeat example 3 if she wants the weekly revenue to be $ 4 , 2 0 0 . Example 3 A manufacturer of hard shell cases for the iPhone knows that the number of cases she can sell each week is related to the price of the cases by the equation x = 1 , 3 0 0 - 1 0 0 p , where x is the number of cases and p is the price per case. What price should she
Repeat example 3 if she wants the weekly revenue

Corn is planted in a rectangular field with a 1 2 row planter ( 1 5 inch row spacing ) using the circuitous pattern with sweeping corners. The crescent shaped areas in the field were left unplanted. The expected corn yield is 1 8 6 bu / ac and the expected value at harvest is 5 $ / bu . The width of the field is 1 , 7 9 3 ft . Assume that the

Determine whether the following functions have a maximum or minimum. For credit show all your work: FOC, SOC and Max or Min value. a ) y = 4 x + 3 b ) y = 2 x + 0 . 5 x 2
Determine whether the following functions have a

A . Find the general solutions of the following separable differential equations, and the corresponding solutions if the initial conditions are given. Express your answers in explicit form whenever possible. d y d x = c s c 2 ( 2 x ) c o t ( 2 x ) 4 y d y d x = 4 - y 2 c o s x 2 y 2 x 2 2 x 2 y ' = s e c 2 y , y ( 4 ) = 4 y ' = 5 x 2 y 2 y 2 x 2 y
A . Find the general solutions of the following

Graph the Curve and Find Velocity and Acceleration: r ( t ) = [ t ^ 2 ] i + [ ( 1 / 4 ) * t ^ 4 ] j , t = 1 ( Graph the curve, and determine the velocity and acceleration vectors at t = 1 . Also, calculate the speed at that time. )

Perform the indicated operation and simplify the result. ( 9 + ( 1 ) / ( x ) ) / ( 2 - ( 1 ) / ( x ) )

ind the derivative of the function. y = log 8 ( x 2 5 x ) y =

evaluate the integral dx / sqrt ( x ^ 2 + 2 x + 5 )

( x ) = C 1 x 2 Inx, x 2 y " - 3 xy ' + 4 y = 0 .

When a number is decreased by 3 0 % of itself, the result is 1 1 2 . What is the number?

Use the substitution of x = 4 tan ( theta ) to solve the integral of 1 2 dx / ( x ^ 2 sqrt ( x ^ 2 + 1 6 ) )

evaluate the indefinite integral: 3 - ( x 3 + x 2 + 7 x ) xdx

x + y 2 = 4 find volume using shell method
x + y 2 = 4 find volume using shell method

Q 4 ) Determine at which points the function f ( z ) = x 3 + i ( : 1 - y : ) 3 differentiable, and write f ' ( z ) at those points.
Q 4 ) Determine at which points the function f (

Show that the series n = 1 ( - 1 ) n + 1 ( 3 + ( - 1 ) n ) n converges and find its sum.
Show that the series n = 1 ( - 1 ) n + 1 ( 3 + (

Write an equation of slope intercept form of ( - 5 , - 3 ) and m = 2 / 3

Let F be the radial force field F = + y j . Find the work done by this force along the following two curves, both which go from ( 0 , 0 ) to ( 1 0 , 1 0 0 ) . ( Compare your answers! ) A . If C 1 is the parabola: x = t , y = t 2 , 0 t 1 0 , then C 1 F * d r = B . If C 2 is the straight line segment: x = 1 0 t 2 , y = 1 0 0 t 2 , 0 t 1 , then C 2 F
Let F be the radial force field F = + y j . Find

a ) Evaluate the integral ( l n x + c o s x 2 3 + s i n x 2 ) d x ( 1 0 points ) Solution: b ) Find f ( x ) in the formula below? ( 1 0 points ) Solution: f ( x ) d x = 3 2 l n x - 1 2 l n ( x + 2 ) + C
a ) Evaluate the integral ( l n x + c o s x 2 3 +

The population ( in millions ) for a country is modeled by P ( t ) = 3 2 0 + 1 . 7 t 0 . 0 0 2 t 2 P ( t ) = 3 2 0 + 1 . 7 t 0 . 0 0 2 t 2 , where t is the number of years since 2 0 0 0 . Step 1 of 2 : What population was predicted for 2 0 1 6 ? Round your answer to one decimal place and, if necessary, round any intermediate calculations to six

[ 1 0 ] 4 . The two lines given below are skew ( you should know how to prove this ) : L 1 : x = 5 + 4 t , y = - t , z = 1 + 2 t , L 2 : x = 7 + , y = 2 - 3 , z = - 1 + 4 Find the equation of the plane that contains L 1 and does not intersect L 2 . Show work and give clear explanation for full credit.
[ 1 0 ] 4 . The two lines given below are skew (

Use vectors to determine whether the points are collinear. ( 0 , - 2 , - 5 ) , ( 3 , 4 , 4 ) , ( 2 , 2 , 1 ) .
Use vectors to determine whether the points are

B . Find the general solution of the following linear differential equations. Express your general solution explicitly if convenient, otherwise leave your answer in implicit format. If the initial conditions are given, find the corresponding particular solutions. x y ' ( 1 x ) y = e - x x 2 Show all images Show all images Show all images done
B . Find the general solution of the following

Determine the average cost function ? b a r ( C ) ( x ) = C ( x ) x . To find where the average cost is smallest, first calculate ? b a r ( C ) ' ( x ) , the derivative of the average cost function. Then use a graphing calculator to find where the derivative is 0 Check your work by finding the minimum from the graph of the function ? b a r ( C ) (
Determine the average cost function ? b a r ( C )

Question 2 1 pts A cube measures 1 5 . 6 2 5 cm ^ ( 3 ) and has a mass of 6 6 . 9 g . Calculate the density of the material that composes the cube. 1 0 . 7 ( g ) / ( c ) m ^ ( 3 ) 4 . 2 8 ( g ) / ( c ) m ^ ( 3 ) 0 . 2 3 4 ( g ) / ( c ) m ^ ( 3 ) 2 6 . 7 ( g ) / ( c ) m ^ ( 3 )

Use implicit differentiation to find del z d elx and del z d ely. d e l z d e l x = x 4 y 8 z 8 = 8 x y z d e l z d e l y = 8 x z - 8 y 7 8 z 7 - 8 y
Use implicit differentiation to find del z d elx

What is the value of the definite integral 9 4 ( 3 t 1 / 2 2 t 1 / 2 ) dt ? Enter your answer as an exact fraction if necessary. Provide your answer below:

give two important areas of application for 2 nd order linear equation with constant coeficients

What is 3 1 1 ( 3 x + 0 . 5 5 x ) dx ? Round your answer answer to TWO decimal places.

under certain environmental conditions, the temperature of the human skin is lower than the core temperature of the body

Evaluate the integral. 3 / 2 8 1 t 2 dt 1 / 2

Derivative of e ^ ( - 3 t )

if z = 3 ln ( 2 x + y ) , then dz / dx is

f ( x ) = lim x 0 3 e x - 3 x \ table [ [ x , - 1 . 2 , - . 5 , - . 0 0 1 , 1 . 2 , . 5 ] , [ f ( x ) , , , , , ] ]
f ( x ) = lim x 0 3 e x - 3 x \ table [ [ x , - 1

use the shell method to set up and evaluate the integral y = x on [ 0 , 2 ]

If lim x x 6 x 2 2 0 0 - 4 x - k x 2 = 1 2 , then k = a ) 3 b ) - 3 c . 1 2 d . - 1 2 e . - 3
If lim x x 6 x 2 2 0 0 - 4 x - k x 2 = 1 2 , then

Evaluate the following Definite Integral. If it does not exist, enter DNE. 0 3 x 1 + 3 xdx =

Need expert on that Use Broyden's method to solve the nonlinear system x 2 y 2 s i n ( x y ) = 1 1 x y c o s ( x y ) = 5 Try at least two different starting points ( or more, if needed to find a solution ) . From your two starting points was the root the same?
Need expert on that Use Broyden's method to solve

Given f ( x ) = ( 1 / 2 0 ) ( x + 1 ) ^ 3 for X from 0 . 0 to 2 . 0 ( continuous ) . What is F ( x ) ? Question 1 Select one: a . ( 1 / 8 0 ) * ( x + 1 ) ^ 4 b . ( 1 / 2 0 ) ( x + 1 ) ^ 3 c . ( x + 1 ) ^ 2 / 2 d . 1 e . ( x + 1 ) ^ 4 / 4

Use part one of the fundamental theorem of calculus to find the derivative of the function. h ( x ) = x z 2 z 4 + 7 dz 1

Find conditions on the constants A , B , C , and D such that the equation ( A x + B y ) d x + ( C x + D y ) d y = 0 is exact. 9 . Find conditions on the constants A , B , C , D , E , and F such that the equation ( A x 2 + B x y + C y 2 ) d x + ( D x 2 + Exy + F y 2 ) d y = 0 is exact.
Find conditions on the constants A , B , C , and

Dilate quadrilateral ABCD using center P and your scale factor. Complete the table. \ table [ [ Ratio , P A ' P A , P B ' P B , P C ' P C , P D ' P D
Dilate quadrilateral ABCD using center P and your

Use implicit differentiation to find d y d x . x t a n ( x y ) = - 3 d y d x =
Use implicit differentiation to find d y d x . x

Find the first derivative with respect to x of this function: f ( x ) = ln ( 1 x )

( b ) l o g 1 6 ( 1 3 )
( b ) l o g 1 6 ( 1 3 )

Evaluate. ( Use C for the constant of integration. ) Sqrt 2 5 - x ^ 2 / X ^ 2

Find g ( f ( x ) ) given that f ( x ) = 4 x 7 and g ( x ) = 3 x ! x + 1

1 ) how should find phase line how should should i know when is equilibrium point is stable unstable, semistable. Consider the following autonomous equation: dy / dt = ( e ^ y 1 ) ( 4 y ^ 2 ) ( y 3 ) ^ 2 ( a ) Find the equilibrium points ( b ) Draw the phase line ( c ) Classify the equilibrium points as stable, semistable, or un - stable. ( d )

integral form 1 to 2 and integral from 1 to 3 { xy ^ 3 ex ^ 2 y ^ 2 } dxdy

Let R be the region bounded by the curves y = x 3 , y = x 2 + 4 , and the y - axis. a ) Find the area of the region. b ) Find the total perimeter of the region. c ) Find the volume of the solid generated by revolving the region about the y - axis. d ) Find the volume of the region whose base is in R , and whose cross sections perpendicular to the
Let R be the region bounded by the curves y = x 3

Solve for y . y - 7 3 - 9 y + 6 4 = - 2 3 Simplify your answer as much as possible. y =
Solve for y . y - 7 3 - 9 y + 6 4 = - 2 3

Question Evaluate the limit lim x - 3 ( - 4 | x + 3 | - 3 ( x + 3 ) ) . Select the correct answer below: - 4 3 0 4 3 8 3 The limit does not exist. Question Evaluate the limit . lim x 1 8 x - 1 8 x + 1 5 2 - 3 3 2 Select the correct answer below: - 3 3 2 3 3 - 2 3 3 2 3 3 2 3 3 2 3 3 2
Question Evaluate the limit lim x - 3 ( - 4 | x +

Calculate the angle between the two vectors i + 2 j + 3 k and 3 i - 2 j + k . Enter your answer in the box below, rounded to the nearest degree ( enter only the number without any degree symbol ) . Answer:
Calculate the angle between the two vectors i + 2

You are given the four points in the plane A = ( - 5 , - 5 ) , B = ( - 1 , 3 ) , C = ( 3 , - 6 ) and D = ( 6 , 7 ) . The graph of the function f ( x ) consists of the three line segments A B , B C and C D . Find the following integral by interpreting it in terms of sums and / or differences of areas of elementary figures from drawing the graph f (
You are given the four points in the plane A = (

Evaluate In 3 7 1 4 / 1 . 0 3 ^ 3

Determine the value of the following limits , if they exist. If infinite, specify either or - . ( If an answer does not exist, enter DNE. ) a . lim x 3 | 2 x + 6 | | x 3 + 2 7 | x + 3 = b . lim x 3 + | 2 x + 6 | | x 3 + 2 7 | x + 3 = c . lim x 3 | 2 x + 6 | | x 3 + 2 7 | x + 3 =

Find the equations of any vertical asymptotes. f ( x ) = x 2 - x - 6 x 2 - 2 x - 8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A . The vertical asymptote ( s ) is / are located at x = 7 . ( Type an integer or a simplified fraction. Use a comma to separate answers as needed. ) B . There are no
Find the equations of any vertical asymptotes. f

Question Define R as the region bounded by the functions f ( x ) = 2 and g ( x ) = e - x 2 between x = 0 and x = 4 . If R is rotated around the x - axis, what is the volume of the resulting solid? Submit an exact answer in terms of e and . Provide your answer below:
Question Define R as the region bounded by the

Total cost is C = 8 7 0 0 + 4 . 6 5 q and total revenue is R = 5 . 4 0 q , both in dollars, where q represents the quantity produced. ( a ) What is fixed cost? The fixed cost is $ ( b ) What is the marginal cost per item? The marginal cost is $ ( c ) What is the price at which this item is sold? The selling price is $ ( d ) For what production
Total cost is C = 8 7 0 0 + 4 . 6 5 q and total

Let f ( x ) = x 2 - 5 x + 6 x 2 - 2 x ( a ) Analyze lim x 0 - f ( x ) , lim x 0 + f ( x ) , lim x 2 - f ( x ) , and lim x 2 + f ( x ) . ( b ) Identify and describe any points of discontinuity of f ( x ) over the interval ( - , ) . ( c ) Describe how the graph of f ( x ) will appear at the points x = 0 and x = 2 .
Let f ( x ) = x 2 - 5 x + 6 x 2 - 2 x ( a )

Differenti ate the function. u ( t ) = ( 9 ) / ( \ pi ) - \ sqrt ( 1 3 )

find the slope, if it exists, of the line containing the pair of points ( 8 , - 2 ) and ( - 8 , - 2 )

Transsexual individuals are always born with one or more

Deriving a Complicated Function Part I Suppose we have the function: f ( x ) = 4 xe ^ ( cos ( 3 x + 1 ) ) + sin ( x ) What is the formula for f ( x ) ?

Use the fundamental Theorem of Calculus to find Integral pi to 3 pi / 2 e ^ - ( cos ( q ) ) . sin ( q ) dq =

3 . 2 . 3 y = 2 x 1 - x 2 Simplify your answer.
3 . 2 . 3 y = 2 x 1 - x 2 Simplify your answer.

( 1 + y 3 ) y ' = x 2 Let f ( x , y ) = x ^ 2 / 1 + y 3 . Find the derivative of f .

Factoring out a binomial from a polynomiak GCF Rewrite the expression by factoring out ( y + 4 ) . 2 y ^ ( 2 ) ( y + 4 ) + 5 ( y + 4 )

1 1 . Suppose a bacterial culture initially has 1 2 0 cells. After 2 hours, the population has increased to 5 0 0 . Find an equation for the population at any time. What will the population be after 8 hours?

can you do # 2 I want to check my answer and it's not in the book bc its an even number. I got - 9 . 1 5 / 3 .
can you do # 2 I want to check my answer and it's

Find the domain. s ( t ) = t ^ - 3 + t ^ 7

find dy / dx for x + tan ( xy ) = 4

Find parametric equations for the line. ( Use the parameter t . ) the line through the points ( 5 , 2 , 5 ) and ( 1 , 9 , 6 )

Find the indicated derivative. d p d q for p = q 2 + 2 4 q - 5 d p d q = 8 q 2 - 1 0 q - 8 ( 4 q - 5 ) 2

Select all of the ordered pairs that make the inequality y > x ^ ( 2 ) + 3 x - 4 true. ( 0 , 0 ) ( 2 , 1 ) ( - 2 , - 1 ) ( - 5 , - 1 )

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