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Mathematics Questions and Answers May 12, 2018

Expert-verified solutions to help you succeed

Use a graphing calculator to estimate the intervals on which f ( x ) = 5 x 3 - 7 x 4 3 is increasing and the intervals where f is decreasing. ( Enter your answer using interval notation. Round your answers to three decimal places. ) increasing decreasing
Use a graphing calculator to estimate the

\ int _ 0 ^ { \ sqrt [ 3 ] { 7 } } y ^ 2 e ^ { y ^ 3 } dy \ :

( a ) If P is the point ( 1 5 , 1 , 4 7 0 ) on the graph of V , find the slopes of the secant lines P Q when Q is the point on the graph with t = 5 , 1 0 , 2 0 , 2 5 , and 3 0 . Slopes of secant lines passing through P ( 1 5 , 1 , 4 7 0 ) and Q ( t , V ( t ) ) can be calculated using the following. m s e c = V ( t ) - 1 , 4 7 0 t - 1 5 We begin by
( a ) If P is the point ( 1 5 , 1 , 4 7 0 ) on

A graphing calculator is recommended. Use your graphing calculator to graph the following four equations simultaneously on the window - 1 0 , 1 0 by - 1 0 , 1 0 . y 1 = 3 x + 7 y 2 = 3 x + 5 y 3 = 3 x - 5 y 4 = 3 x - 7 Need help graphing
A graphing calculator is recommended. Use your

\ table [ [ Entered , Answer Preview,Result ] , [ y ' ' ' ' - 1 6 * * y ' ' ' + 7 0 * * y ' ' - 1 3 6 * * y ' + 2 8 9 * * y = 0 , y ' ' ' ' - 1 6 y ' ' ' + 7 0 y ' ' - 1 3 6 y ' + 2 8 9 y = 0 , incorrect ] , [ y = c 1 * * [ e 4 * * x ] * * c o s ( x ) + c 2 * * [ e 4 * * x ] * * s i n ( x ) + c 3 * * x * * [ e 4 * * x ] * * c o s ( x ) + c 4 * * x
\ table [ [ Entered , Answer Preview,Result ] , [

The function h is given by h ( x ) = 4 x 3 + 3 x 2 - 6 x + 1 . What is the absolute maximum value of h on the closed interval - 2 , 1 ( y - value ) What is the value c guaranteed by the Mean Value Theorem for y = x 2 - 4 x + 5 on - 1 , 3 Given the function f ( x ) = 1 3 x 3 - 2 x 2 - 5 x + 2 find the value c guaranteed by the Mean Value Theorem
The function h is given by h ( x ) = 4 x 3 + 3 x

ork Solve the following inequality. Write the solution set using ( 3 x + 3 ) / ( 7 ) - ( 3 x - 1 ) / ( 9 ) > = - 3

( 0 , - 2 , 0 ) rectangular to spherical

differentiate the function f ( t ) = 1 4 t 5 2 5 t 2 + e 5

Evaluate the integral. ( Use C for the constant of integration. ) 1 0 ln ( 3 x ) dx

find the domain of f ( x ) = ( x + 9 ) / ( x ^ ( 2 ) + 2 x - 3 )

Ben drove 5 8 4 miles in 8 . 2 hours. What was his average rate of speed?

The profit ( in dollars ) from the sale of x lawn mowers is P ( x ) = 6 0 x - 0 . 0 6 x 2 - 4 5 0 . ( A ) Find the average profit per mower if 3 0 mowers are produced. ( B ) Find the marginal average profit at a production level of 3 0 mowers, and interpret the results. ( C ) Use the results from parts ( A ) and ( B ) to estimate the average
The profit ( in dollars ) from the sale of x lawn

Evaluate 1 4 f ( t ) d t , where f ( t ) is continuous on [ 1 , 4 ] , and F ' ( t ) = f ( t ) and F ( 1 ) = 2 , and F ( 4 ) = 5 7 1 0 - 3 3
Evaluate 1 4 f ( t ) d t , where f ( t ) is

Given the equation y = 5 x 1 5 , how will y change if x does the following? ( b ) decreases by 3 units

Year 2 0 1 5 / 2 0 1 6 / 2 0 1 7 / 2 0 1 8 / 2 0 1 9 Sales 1 5 . 8 0 / 1 5 . 5 2 / 1 5 . 8 6 / 1 6 . 5 8 / 1 6 . 3 8 from 2 0 1 5 to 2 0 1 9 , were there any one - year intervals during which the average rate of change was negative? If so , when? 2 0 1 5 - 2 0 1 6 2 0 1 6 - 2 0 1 7 2 0 1 7 - 2 0 1 8 2 0 1 8 - 2 0 1 9 No such intervals

Connecting the Communication Device Wth the communication device peirted loward your home planet, you realoon, to your dismay, that the cords have been disconnocted from the device. "Compuler, how do I plag in those cables", you ask. Hour compuler responds that the directions ( translaped inlo mathomasics ) suggest that you orfer the cebleat from
Connecting the Communication Device Wth the

Solve the IVP d x d t = ( 1 - 2 t ) x 2 with x ( 0 ) = - 1 6 . What is the interval in which the solution is defined?
Solve the IVP d x d t = ( 1 - 2 t ) x 2 with x (

Find the derivative of the function y = 5 x 3 4 x 2 Select the correct answer below: 4 x 2 ( ln 5 ) ( 5 x 3 ) 8 x 1 6 x 2 5 x 3 ( 1 2 x 4 ( ln 5 ) 8 x ) 1 6 x 4 5 x 3 ( 4 x 2 ( ln 5 ) 8 x ) 1 6 x 2 1 2 x 4 ( ln 5 ) ( 5 x 3 ) 8 x 1 6 x 2

If f ( x ) = 3 x + 5 / 5 x + 3 , f ( x ) = 3 x + 5 5 x + 3 , , find: f ' ( x ) f ( x ) = f ' ( 3 ) f ( 3 )

whats the derivitive of 9 x ^ 2

Evaluate the limit using the appropriate Limit Law ( s ) . ( If an answer does not exist, enter DNE. lim x 4 ( 2 x 3 - 4 x 2 + x - 7 )
Evaluate the limit using the appropriate Limit

Consider the following first order linear homogeneous patrial differential equation. du / dt - 5 du / dx = 0 Shoe that if f is any differentiable function of a sibgle variable, then u ( x , t ) = f ( x + 5 t ) is a solution of the PDE

For what value of the constant c is the function f ( x ) continuous on the interval ( , ) wheref ( x ) = { x 2 4 c if x 4 5 cx 6 c if x > 4 . If the answer in infinity, you can type in INF in the blank. If the answer is negative infinity, you can type - INF. If the answer is does not exist, you can type in DNE. Otherwise, write the number as an

integral sin ( 2 x ) cos ( x ) + sin ( x ) cos ( 2 x ) dx

Sketch the graph of a single function f satisfying all of the following properties: ( i ) lim x - 2 - f ( x ) = ( iii ) lim x 3 + f ( x ) = 3 ( v ) f ( 3 ) = 1 ( ii ) lim x - 2 + f ( x ) = ( iv ) lim x 3 - f ( x ) = 4 ( vi ) Domain is ( - , ) .
Sketch the graph of a single function f

The areas of cross sections of Lake Nogebow at 5 - m intervals are given in the table. \ table [ [ Depth ( m ) , 0 , 5 , 1 0 , 1 5 , 2 0 ] , [ Area ( million m 2 ) , 2 . 2 , 1 . 7 , 1 . 4 , 0 . 7 3 5 , 0 . 2 5 7 ] ] The following figure shows a contour map of the lake. Find the left - endpoint and right - endpoint approximations to the integral of
The areas of cross sections of Lake Nogebow at 5

Solve the integral c o s 7 ( x ) t a n 2 ( x ) d x Enter the constant of integration as c or C .

I need real person to help me with it not an AI please Problem 2 : Graphing a Function ( 2 0 points ) Sketch a possible graph of a function satisfying all of the following properties: f is an odd function with domain - 6 , 6 . f has intervals of continuity: ( 0 , 1 ] , ( 1 , 4 ) , and 4 , 6 . f ( 1 ) = 3 , and f ( 6 ) = 2 . lim x 0 + f ( x ) = 2 .
I need real person to help me with it not an AI

Test the series for convergence or divergence. n = 1 ( - 1 ) n - 1 e 6 n Identify b n . Evaluate the following limit . lim n b n Since lim n b n hat ( v ) v v 0 and b n + 1 n a hat ( v ) b n for all n , the series diverges
Test the series for convergence or divergence. n

integral sqrt ( x ^ 2 - 9 ) / x dx

Use the method of partial fractions to evaluate the following integral. 5 x 3 3 4 3 dx Be sure to place the argument of any logarithmic functions in absolute value signs when submitting your answer.

Evaluate the integral by making the given substitution. ( Use C for the constant of integration. ) e 1 6 x dx , u = 1 6 x

y = ( ( x + 2 ) ( x ^ ( 2 ) - 4 ) ) ^ ( 8 )

Which of the following is the solution to the differential equation 4 7 - 2 = - y with the initial condition ( 0 ) = - 3 ? y = - 1 - 2 VE + 1 @y = - e + - 2 @ 3 = 2 - 5 e * = 2 - 5 6 '

Find the limit lim x 3 2 2

Consider the following. a 1 = 7 , a n + 1 = 8 - a n Calculate, to four decimal places, the first eight terms of the recursive sequence. \ table [ [ n , a n
Consider the following. a 1 = 7 , a n + 1 = 8 - a

What is the quotient of the complex number 5 + 2 i divided by its conjugate?

Determine the average rate of change of B from t = o to t = 3 9 2 a = 2 b

Solve the following initial value problem: d y d t + 0 . 8 t y = 7 t , y ( 0 ) = 4 y ( t ) =
Solve the following initial value problem: d y d

the cartesian coordinates of a point are ( 2 sqrt ( 3 ) , - 2 ) . find polar coordinates

Consider the following functions. f ( x ) = 1 x 5 , g ( x ) = 1 x 9 ( a ) Find ( f + g ) ( x ) . ( f + g ) ( x ) = State the domain of the function. ( Enter your answer using interval notation. ) ( b ) Find ( f g ) ( x ) . ( f g ) ( x ) = State the domain of the function. ( Enter your answer using interval notation. ) ( c ) Find ( fg ) ( x ) . (

Question 3 Let 2 8 f ( x ) = x + 5 x + 8 f - 1 ( - 1 0 ) =

y = l n 1 + s i n 2 ( x ) 2 at x = 4

Find the indicated limit , if it exists. ( If an answer does not exist, enter DNE. Do not use mixed numbers in your answer. ) lim x 5 x 2 + 9 x + 5 8 x 2 - 7 x + 4
Find the indicated limit , if it exists. ( If an

Let one white tile represent + 1 and one black tile represent - 1 . What sum 4 poir does this set of tiles model? Write the addition equation. ( + 4 ) + ( + 3 ) = + 3 ( - 4 ) + ( + 3 ) = - 1 ( + 3 ) + ( + 4 ) = + 7

code class = "asciimath" > Limit [ Divide [ Cbrt [ x ] - 1 , Surd [ x , 4 ] - 1 ] , x - > 1 ]

Given the piecewise function, find the function values. f ( x ) = { 2 x - 2 i f x - 4 8 - 5 x i f x - 4 f ( - 5 ) = [ f ( 0 ) = f ( 1 ) = f ( 3 ) =
Given the piecewise function, find the function

Write an equation in standard form of the horizontal line passing through ( 0 , 0 ) . The equat on in standard form is

Hyperboloid of two sheets of equation with the y - axis as the axis of symmetry,

( 1 point ) Consider the integral 5 2 ( 3 2 + 3 + 3 ) 2 5 ( 3 x 2 + 3 x + 3 ) dx . Reinman sum

Find G ' ( w ) if G ( w ) = 3 8 w 5 + 9 w 4 G ' ( w ) = - 1 0 3 w 5 + 9 4 w 3 4
Find G ' ( w ) if G ( w ) = 3 8 w 5 + 9 w 4 G ' (

Convert the point from rectangular coordinates to cylindrical coordinates. ( 6 , 2 3 , 3 )

Assuming P > = 0 , suppose that a population develops according to the logistic equation dPdt = 0 . 0 6 P 0 . 0 0 0 6 P 2 where t is measured in weeks. Answer the following questions. 1 . The carrying capacity is the limit limt - > \ infty P ( t ) of the population size after a very long time. What is the carrying capacity? Carrying Capacity = 2 .

Determine the value of c so that lim x 7 f ( x ) exists: f ( x ) 1 7 x + c - x + 1 4 for x < 7

f ( x ) = { 1 - x i f x 1 - x 2 + x i f x > 1 evaluate as x 1 : a . the left limit b . the right limit c . the limit lim ? f ( x )
f ( x ) = { 1 - x i f x 1 - x 2 + x i f x style=

? Question Use the distributive property to multiply the polynomials. - 5 x ^ ( 2 ) ( 6 x - 1 )

Find the derivative. y = 7 x + 6 secx Question 6 options: A ) y ' = - 7 x 2 + 6 tan 2 x B ) y ' = 7 x 2 - 6 cosx C ) y ' = 7 x 2 - 6 secxtanx D ) y ' = - 7 x 2 + 6 secxtanx E )

x ^ 2 / 1 6 + y ^ 2 / 1 0 0 - z ^ 2 / 3 6 . Find the intercepts with the three coordinate exes, if they exist.

It costs $ 0 . 5 5 to mail one first class letter. Construct a linear equation and solve to find how much it costs to mail 1 3 letters.

integral of xsin ( mx ) / m

( 1 point ) Let f ( x ) = 1 6 x + 7 , - 3 x 1 0 The domain of f - 1 is the interval A , B where A = and B =
( 1 point ) Let f ( x ) = 1 6 x + 7 , - 3 x 1 0

Let f ( r ) = z - x 2 - y 2 . The equation f ( r ) = 0 describes a cup - shaped surface S . Find the surface normal vector to the surface at point
Let f ( r ) = z - x 2 - y 2 . The equation f ( r

Express the limit as a definite integral. lim n 1 n i = 1 n 8 1 ( i n ) 5 0 1 d x
Express the limit as a definite integral. lim n 1

Integrate sin ^ 5 ( 4 x ) cos ^ 3 ( 4 x ) dx

Problem 1 0 . Under reasonable assumptions, the population of a bacterial culture at time t ( in hours ) is modeled by the function P ( t ) = K P 0 P 0 + ( K - P 0 ) e - r t where P 0 is the size of the bacterial population at time t = 0 , K is the carrying capacity, and r is the growth rate per hour. ( a ) Find the rate of change of the
Problem 1 0 . Under reasonable assumptions, the

A frog can swim at 1 m s . It is on one side of a stream, at Point A and wants to swim to Point B on the other side of the stream, and 1 0 metres downstream. The stream is 5 metres wide and the current is 0 . 5 m s . a ) Calculate the angle, with respect to the shore, the frog must aim to land at point B . ( 5 Marks ) b ) How many seconds will it
A frog can swim at 1 m s . It is on one side of a

Find the distance from the point ( - 5 , - 4 , - 9 ) to the line vec ( a ) ( t ) = ( : 0 , - 4 , 5 : ) t ( : 1 , 8 , 6 : ) .
Find the distance from the point ( - 5 , - 4 , -

integral of e ^ x / ( e ^ x - 1 ) from - 1 to 1

Use the Trapezoidal Rule, the Midpoint Rule and Simpson's Rule to approximate 3 6 1 2 x 4 d x using n = 4 . Enter exact values ( i . e . numerical expressions ) or round your final answers to four decimal places.
Use the Trapezoidal Rule, the Midpoint Rule and

Differentiate. Upper G left parenthesis x right parenthesisG ( x ) equals = ( 7 7 xsquared 2 plus + 5 5 ) left parenthesis 2 x plus StartRoot x EndRoot right parenthesis

AP CALCULUS STUDENT HANDOUT Applying Procedures for U - Substitution The table below gives the same indefinite integrals from the Introductory Activity. This time, let u equal the inside function identified before, determine its differential du , and then use this substitution to construct an equivalent integral in terms of u and du only. Inside
AP CALCULUS STUDENT HANDOUT Applying Procedures

lim x 0 1 / square root x + 1 1 / x

In determining the size of a V belt to be used with an engine, the expression 9 + [ 2 x - ( 8 - 5 x ) ] is used. Simplify this expression. q ,

Simplify: x ( x + 6 ) 1 / 2 ( x + 6 )

\ int \ frac { 1 } { x ^ 2 + 3 } dx

let f ( x ) = 3 sqrt x compute f ( 6 4 )

Explain, using these theorems, why the function is continuous at every number in its domain. g ( v ) = 7 v 1 v 2 + 2 v 6 3 g ( v ) is a rational function, so it is continuous at every number in its domain.g ( v ) is an exponential function, so it is continuous at every number in its domain. g ( v ) is a trigonometric, so it is continuous at every

Do not evaluate the limit . ( a ) Use Definition 2 to find an expression for the area under the curve y = x ^ ( 3 ) from 0 to 1 as a limit .

Question number 1 1 Find the differential equation that has y = C _ { 1 } + C _ { 2 } * x ^ 9 as its general solution.xy ^ prime prime - 8 * y ' = 0 x * y ' - 8 y = 0 xy ^ prime prime - 9 * y ' = 0 xy ^ prime prime + 8 * y ' = 0 x * y ' + 8 y = 0 None of the above.

Solve for t using natural logarithms. 9 = 2 e t Round your answer to three decimal places. t =
Solve for t using natural logarithms. 9 = 2 e t

x = t ^ 2 - 2 , y = t + 1 , - 3 t 3 Eliminate the parameter to find a cartesian equation of the curve.

Evaluate the integral. 2 0 cos ^ 1 3 ( x ) sin ^ 5 ( x ) dx

( 3 x ^ 2 + 9 xy + 5 y ^ 2 ) dx - ( 6 x ^ 2 + 4 xy ) dy = 0 , y ( 2 ) = - 6

Evaluate the following integral. 1 0 1 6 x 2 + 4 0 0 dx Enter your answer as an exact answer.

Find the volume of revolution about the x - axis for the given function and interval. f ( x ) = 5 cos ( x ) , [ 0 , 4 ] Consider the integral used to compute the volume of revolution. 0 4 ( 5 cos ( x ) ) 2 dx

Find dy / dx by implicit differentiation. x ^ 3 ( x + y ) = y ^ 2 ( 9 x y ) dy / dx =

For the graph of y = f ( x ) shown to the right, find the absolute minimum and the absolute maximum over the interval 5 , 9 . Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A . The absolute minimum is at x = and x = ( Round to the nearest integer as needed. Use ascending order. ) B . The
For the graph of y = f ( x ) shown to the right,

Find the radius and the interval of convergence of the series n = 1 ( - 1 ) n 1 n 3 ( x + 2 ) n .
Find the radius and the interval of convergence

Evaluate the limit using continuity. ( Use symbolic notation and fractions where needed. ) lim ( x , y ) ( 5 , 9 ) e ^ x ^ 2 - e ^ ey ^ 2 / x + y

The point P ( 9 , - 2 ) lies on the curve y = 2 / 8 - x . if Q is the point ( x , 2 / 8 - x ) , fin the slope of the secant line PQ for the following values of x

The vector u = 3 2 0 0 , 1 4 1 0 , 2 2 4 0 gives the numbers of hamburgers, chicken sandwiches, and cheeseburgers, respectively, sold at a fast - food restaurant in one week. The vector v = 1 . 3 0 , 2 . 8 0 , 1 . 9 0 gives the prices ( in dollars ) per unit for the three food items. Find the dot product u v , in dollars. ( Round your answer to

Q 5 . Given W = 2 3 r 3 h 4 . A percentage error of 2 % and 1 % are committed in measuring r and and h respectively, find the maximum percentage error in calculating. W . [ 6 marks ] Q 6 . Locate and classify all critical points for f ( x , y ) = 2 y 2 + x 4 - 3 x y [ 6 marks ]
Q 5 . Given W = 2 3 r 3 h 4 . A percentage error

Practice similar Score Find the scalar and vector projection of the vector b = ( : - 5 , - 2 , - 1 : ) onto the vector a = ( : 3 , 5 , 1 : ) . Scalar projection ( i . e . , component ) : Vector projection )
Practice similar Score Find the scalar and vector

Use the definition of the derivative to compute $$ ( x ) = x 2 4 . limh 0 ( x + h ) ( x ) h Start over We know $$ ( x ) = limh 0 ( x + h ) ( x ) h . Replace $$ ( x + h ) with its value.

Reparameterize the curve vec ( r ) ( t ) = ( : t 3 , ( t 2 - 4 ) 3 2 , 3 t 2 : ) , t 2 with respect to arc length measured from the point where t = 2 , in the direction of increasing t .
Reparameterize the curve vec ( r ) ( t ) = ( : t

Draw the level curves for f of values of c . f ( x , y ) = y c s c ( x ) , c = 0 , 1 , 2 ( Graph the level curves using the graphing utility. Add more than one curve to the graph if necessary. )
Draw the level curves for f of values of c . f (

Find the volume of the solid generated by revolving the region bounded by y = x , y = 0 and x = 3 about the line x = 6 . You may use the method of your choice: disk, washer or shell. Give your answer rounded to 3 decimal places.
Find the volume of the solid generated by

Differentiate. g ( x ) = 2 x - 3 9 x + 4 + x 3 g ' ( x ) =
Differentiate. g ( x ) = 2 x - 3 9 x + 4 + x 3 g

g = 9 ( 2 8 ) - 2 ( 1 8 )

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