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Mathematics Questions and Answers June 14, 2018

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[ - / 6 . 2 5 Points ] Find a formula for the general term a n of the sequence, assuming that the pattern of the first few terms continues. ( Assume that n begins w { 1 , - 1 3 , 1 9 , - 1 2 7 , 1 8 1 , cdots } a n = Need Help? Vewing Saved Work Revert to Last Response
[ - / 6 . 2 5 Points ] Find a formula for the

Find the surface area of revolution about the x - axis of y = 6 sin ( 4 x ) over the interval 0 < x < \ frac { \ pi } { 4 }

Find the open intervals on which the function f ( x ) = x 1 0 1 - x 2 is increasing or decreasing. The safe points will be calculated from these intervals. If the function is never increasing or decreasing, provide an input of NA to your computer. Increasing Interval: Decreasing Interval:

What is the area of the region bounded by the curves ( ) = 2 f ( x ) = x 2 and ( ) = + 2 g ( x ) = x + 2 ? Select one: a . 3 3 b . 4 . 5 4 . 5 c . 7 . 5 7 . 5 d . 1 0 . 5

2 7 - 3 4 Explain, using Theore function is continuous at ever the domain. 2 7 . f ( x ) = x 2 x 4 2 2 2 9 . h ( t ) = c o s ( t 2 ) 1 - e t 3 0 . B ( u ) = 3 u - 2 2 2 u 3 3 1 . L ( v ) = v l n ( 1 - v 2 ) 3 3 . M ( x ) = 1 1 x 2
2 7 - 3 4 Explain, using Theore function is

r = 3 x 2 y 2 and ( x , p ) changes from ( 1 , 2 ) to 1 . 0 5 , 1 . 9 , compare the values of 2 r and do . ( flourd your arrwers to four decimal places. d r = Ave
r = 3 x 2 y 2 and ( x , p ) changes from ( 1 , 2

The function f ( x ) is a polynomial and hence it is defined for all real numbers. Its first derivative is given by: f ' ( x ) = - 5 ( x + 3 ) ( x - 3 ) 2 ( x - 5 ) 3 . List all local extreme points for the function f ( x ) .
The function f ( x ) is a polynomial and hence it

Solve the equation. StartFraction x plus 1 Over 6 EndFraction plus StartFraction x plus 1 Over 5 EndFraction equals 1

2 . 2 . 8 . Solve y ' ' - 8 y ' 1 6 y = 0 for y ( 0 ) = 2 , y ' ( 0 ) = 0 .
2 . 2 . 8 . Solve y ' ' - 8 y ' 1 6 y = 0 for y (

lim x - - > infinity 5 x + sqrt ( 2 5 x ^ 2 - x )

QUESTION 4 * 1 POINT Find the upper bound for the error using the midpoint rule with n = 5 subintervals. - 2 2 ( s i n ( x ) ) d x Round your answer t o the nearest hundredth a s necessary. Provide your answer below: Error bound
QUESTION 4 * 1 POINT Find the upper bound for the

SCalcET 9 1 2 . 3 . 0 5 2 . A boat sails south with the help of a wind blowing in the direction 5 3 6 E with magnitude 5 0 0 lb . Find the work ( in f t - l b ) done by the wind as the boat moves 1 1 0 ft . ( Round your answer to the nearest whole number. )
SCalcET 9 1 2 . 3 . 0 5 2 . A boat sails south

Consider the following function. f ( x ) = 4 x 3 + 1 5 x 2 - 1 5 0 x + 3 ( a ) Find the intervals o n which f i s increasing. ( E n t e r your answer using interval notation. ) Find the interval o n which f i s decreasing. ( E n t e r your answer using interval notation. ) ( b ) Find the local minimum and maximum values o f f . local minimum value
Consider the following function. f ( x ) = 4 x 3

Question 1 1 ( 3 points ) Evaluate the l i m i t : lim x - 6 x 2 + 9 x + 1 8 x + 6 Enter a whole, fraction o r decimal number, o r DNE for does not exist o r undefined.
Question 1 1 ( 3 points ) Evaluate the l i m i t

Find the l i m i t o r show that i t does not exist. lim x c o s 2 ( x ) x 2 + 1
Find the l i m i t o r show that i t does not

Find the limit . Find the limit . lim x 0 ( c o s ( 2 x ) ) 1 x 2 lim x ( x 7 x 2 ) x
Find the limit . Find the limit . lim x 0 ( c o s

multiply Simplify if possible 9 x ^ 4 - 7 2 x / 3 x ^ 2 - 1 2 * x ^ 2 + x - 2 / 4 x ^ 3 + 8 x ^ 2 + 1 6 x

Use Euler's method with step size h = 0 . 4 to approximate y ( 1 . 8 ) where y ( x ) is a solution of the initial - x Need Help?
Use Euler's method with step size h = 0 . 4 to

N ( t ) equals Upper N 0 e Superscript kt ( Type an expression using t as the variable and in terms of e . ) Part 2 ( b ) The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1 0 0 0 mosquitoes initially and there are 1 4 0 0 after 1 day, what is the size of the colony after 2 days ?

Find the area of the region bound by the curves y = 5 - x ^ 2 , y = 1

To make a poster of at least one solid which is used to make a soma cube

3 - 3 0 Differentiate. 3 . y = ( 4 x 2 3 ) ( 2 x 5 )
3 - 3 0 Differentiate. 3 . y = ( 4 x 2 3 ) ( 2 x

The surface of a mountain is modeled by the equation h ( x , y ) = 9 0 0 0 0 . 0 0 1 x 2 0 . 0 0 4 y 2 . A mountain climber is at the point ( 5 0 0 , 7 0 0 , 6 7 9 0 ) . In what direction should the climber move in order to ascend at the greatest rate?

Find the domain and range of the given function. Explain your answers. f ( x ) = - 3 2 - x 2 What is the domain of the function? A . All real numbers x < 2 B . All real numbers x 2 C . All real numbers x > 2 D . All real numbers x 2

Let vec ( r ) ( t ) = ( : - 2 t 5 + 1 , e t , - 4 s i n ( 4 t ) : ) Find vec ( r ) ( t ) d t + C vec ( r ) ( t ) d t = , , >
Let vec ( r ) ( t ) = ( : - 2 t 5 + 1 , e t , - 4

Required information Consider the following initial - value problem over the interval t = 0 t o t = 2 , where y ( 0 ) = 1 . d y d t = y t 3 - 1 . 5 y NOTE: This i s a multi - part question. Once a n answer i s submitted, you will b e unable t o return t o this part. Solve using Euler's method with h = 0 . 5 and 0 . 2 5 . For h = 0 . 5 ,
Required information Consider the following

A bacteria culture starts with 3 0 0 0 bacteria and the population doubles after 4 hours. The number of bacteria after t hours is given by the model P ( t ) = P 0 e r t Determine the number of bacteria after 1 0 hours. Possibilities: ( a ) ~~ 1 2 , 0 0 0 ( b ) ~~ 1 6 , 9 7 0 ( c ) ~~ 1 8 , 0 8 0 ( d ) ~~ 1 9 , 7 0 0 ( e ) ~~ 2 2 , 5 5 0
A bacteria culture starts with 3 0 0 0 bacteria

When we estimate distances from velocity data it is sometimes necessary to use times t 0 , t 2 , t 2 , t 3 , dots, that are not equally spaced. We can still estimate distances using the time periods t i = t i - t i - 1 . For example, on May 7 , 1 9 9 2 , the space shutte Endenrour wan launched on mission STS - 4 9 , the purpose of which was to
When we estimate distances from velocity data it

Let f b e the R 3 - R function defined b y f ( x , y , z ) = x y z ( a ) Determine the rate o f increase o f f a t the point ( e , 1 , 1 ) i n the direction o f the vector ( 3 , - 2 , 1 ) . ( b ) Determine the maximum rate o f increase o f f a t ( e , 1 , 1 ) . I n which direction i s the maxi - mum rate o f increase? ( c ) A t the point ( e , 1 ,
Let f b e the R 3 - R function defined b y f ( x

Several years ago, ADIF Distributors purchased a brand new cargo plane to increase their coast to coast thipping capabilities. When the plane mas new, it was valued at 1 6 5 million dollars. However, it has depreciated in value over time. After owning and using the plane for 4 years, ADIF had it inipected and found that it was now valued at 1 5 0
Several years ago, ADIF Distributors purchased a

Sketch the region bounded by the graphs of the functions and find the area of the region. f ( x ) = x 2 4 x 4 and g ( x ) = 2 x 7 h ( x ) = 3 s i n x and j ( x ) = 3 2 t a n x on the interval - 3 , 3 . Find the volume of the solid formed by revolving the region bounded by the graph y = - x 2 4 x and y = 3 about the line y = 1 .
Sketch the region bounded by the graphs of the

Consider the following. ( If an answer does not exist, enter DNE. ) f ( x ) = 2 x 3 - 9 x 2 1 2 x - 4 Find the interval ( s ) on which f is concave up . ( Enter your answer using interval notation. ) Find the interval ( s ) on which f is concave down. ( Enter your answer using interval notation. ) Find the inflection point of f . ( x , y ) = ( )
Consider the following. ( If an answer does not

1 9 6 0 . Derivatives Find and simplify the derivative of the following functions. 2 7 ) f ( x ) = xe ^ ( - x )

[ - 3 . 3 4 Points ] Determine whether the geometric series i s convergent o r divergent. I f i t i s convergent, find the sum. ( I f the quantity diverges, enter DIVERGES. ) n = 1 ( - 8 ) n - 1 9 n
[ - 3 . 3 4 Points ] Determine whether the

Find the derivative of h ( x ) = ( 2 x - 2 ) 2 ( - 3 x - 2 ) 2 h ' ( x ) =
Find the derivative of h ( x ) = ( 2 x - 2 ) 2 (

[ - / 1 Points ] Find the indefinite integral. ( Use C for the constant of integration. ) = 7 x 6 5 ( x 7 5 x ) 2 d x Show My Work ( Optional )
[ - / 1 Points ] Find the indefinite integral. (

Use the trapezoidal rule with 4 trapezoids to find an approximation for 0 2 1 1 x 2 d x . A ~~ 1 1 1 1 3 0 A ~~ 7 3 1 0 4 A ~~ 1 9 4 A ~~ 2 8 7 2 6 0
Use the trapezoidal rule with 4 trapezoids to

Find r ( t ) . r ( t ) = 8 sqrt ( t ) i + t ^ 2 sqrt ( t ) j + ln ( t ^ 2 ) k

Express the sum x + x ^ 2 - x ^ 3 in terms of geometric series ( hint: group and ) .

[ - / 0 . 1 6 Points ] 0 / 1 0 0 Submissions Used Evaluate the integral. ( Remember the constant of integration. ) 1 9 l n ( x ) x 4 ( l n ( x ) ) 2 2 d x Need Help?
[ - / 0 . 1 6 Points ] 0 / 1 0 0 Submissions Used

Problem 2 2 . Find the average revenue function o f the given C ( x ) = 1 4 5 + 1 . 1 x and R ( x ) = 5 x - 0 . 0 2 x 2
Problem 2 2 . Find the average revenue function o

The algebraic expression 0 . 0 1 2 5 x 0 . 0 1 7 5 ( 8 0 0 0 - x ) = 0 . 0 0 5 x 1 4 0 use each form of the algebraic expression to determine the total intrest for the month if the balance on the card charging 1 5 % is $ 7 6 0 0 . Find the total interest for the month using the given algebraic expression.

Find a ) any critical values and b ) any relative extrema. g ( x ) = - x 3 3 x - 5 a ) Select the correct choice below and, if necessary, fill in the answer box within your choice A . The critical value ( s ) of the function is / are ( Use a comma to separate answers as needed ) B . The function has no critical values.
Find a ) any critical values and b ) any relative

Use the limit definition of the derivative to find the instancaneous rate of change of f ( x ) = 7 x 2 5 x 2 at x = 3
Use the limit definition of the derivative to

R f ( x , y ) d A = c d [ a b f ( x , y ) d x ] d y We are given the function f ( x , y ) = x + 6 y . Therefore, the integral we are interested in , over the rectangular region 1 x 2 and 0 y 1 is as follows. 0 1 [ 1 2 ( ) d x ] d y
R f ( x , y ) d A = c d [ a b f ( x , y ) d x ] d

Use Simpson's rule with n = 4 to approximate 1 5 s i n ( x ) x d x . 1 5 s i n ( x ) x d x ~~ Keep at least 2 decimal places accuracy in your final answer
Use Simpson's rule with n = 4 to approximate 1 5

to differentiate. y = ( 3 - x 2 ) ( x 3 9 x 7 ) a . Apply the Product Rule. Let u = 3 - x 2 and v = x 3 9 x 7 . ( : d d x ( u v ) = ( 3 - x 2 ) ( ) ( x 3 9 x 7 ) } b . Multiply the factors of the original expression, u and v , to produce a sum of simpler te y = Find y ' y ' =
to differentiate. y = ( 3 - x 2 ) ( x 3 9 x 7 ) a

Determine whether these improper integrals diverge o r converge. For each one that converges, find its value: a . 3 2 x 3 d x b . - 1 1 1 x 4 d x
Determine whether these improper integrals

Integrate: 4 8 x 3 8 0 x 2 7 1 x 1 2 6 1 6 x 2 2 5 d x
Integrate: 4 8 x 3 8 0 x 2 7 1 x 1 2 6 1 6 x 2 2

I n this exercise, w e consider parabolas whose axis o f symmetry need not b e parallel t o the y - axis. ( a ) Find the equation o f the parabola with focus ( 1 4 , 0 ) and directrix x = - 1 4 . ( b ) Find the equation o f the parabola with focus ( 2 , 7 ) and directrix 3 x + 4 y = 1 a x 2 + b x + c y 2 + d y + exy = f . L b e the line with
I n this exercise, w e consider parabolas whose

Solve the following equation for x 2 e x 3 = 8 x = 4 e - 3 x = l n ( 5 ) 2 x = 4 e 3 x = l n ( 4 ) - 3 Question 8
Solve the following equation for x 2 e x 3 = 8 x

SCalcET 8 1 3 . 4 . 0 1 0 . Find the velocity, acceleration, and speed of a particle with the given position function.r ( t ) = 4 cos ( t ) , 3 t , 4 sin ( t ) v ( t ) = a ( t ) = | v ( t ) | =

Find the region i n the x y - plane i n which the function, f ( x , y ) = l n ( 2 x - y ) , i s continuous. Write your answer i n inequality notation. The region i s { ( x , y ) | , }
Find the region i n the x y - plane i n which the

C for the constant o f integration. ( s e c 2 ( t ) i + t ( t 2 + 1 ) 6 j + t 4 l n ( t ) k ) d t
C for the constant o f integration. ( s e c 2 ( t

determine the points of intersection if exist. a ) y = - 2 x + 4 y = x ^ 2 - 6 x + 1 0 b ) f ( x ) = x ^ 2 - 6 x - 7 g ( x ) = 2 x ^ 2 - 2 x - 1 2

lim x - 1 3 x 3 x 2 - 8 x - 9 =
lim x - 1 3 x 3 x 2 - 8 x - 9 =

Find the volume of the shape generated by f ( x ) = x 2 x 2 1 from 0 , 3 on the x - axis, rotated about the x - axis. To receive full credit, make sure to show all calculusbased steps, justification for your limits of integration, all the arithmetic computations, and provide a sketch of the region, the shape generated, and a representative slice /
Find the volume of the shape generated by f ( x )

How many years ( to two decimal places ) will it take an investment of $ 3 1 0 0 to grow to $ 5 0 6 0 it it is invested at 8 . 2 9 % compounded continuously? years
How many years ( to two decimal places ) will it

Evaluate ( x 2 3 ) 2 0 x d x 1 2 ( x 2 3 ) 2 1 c 1 2 1 ( x 2 3 ) 2 1 c 1 4 2 ( x 2 3 ) 2 1 c 1 3 8 ( x 2 3 ) 1 9 c
Evaluate ( x 2 3 ) 2 0 x d x 1 2 ( x 2 3 ) 2 1 c

Suppose that an object is projected in such a way that its height above the ground in feet after t seconds is given by s ( t ) = - 1 6 t 2 4 8 t 1 8 Find the maximum height of the object. Do not write the units in your answer.
Suppose that an object is projected in such a way

The plane containing the point ( 4 , - 7 , 7 ) and parallel t o the plane - 5 x - 8 y - 2 z = 6 has equation A x + B y + C z = D . I f A = - 5 find the following: B = C = D =
The plane containing the point ( 4 , - 7 , 7 )

Evaluate 2 e x x d x Select one: a . 2 x e x - 2 e x b . 2 x e x 2 e x c c . 2 x e x - 2 e x c d . 2 x e x 2 e x
Evaluate 2 e x x d x Select one: a . 2 x e x - 2

What is the distance from the point ( 7 , 4 , - 7 ) to the x z - plane? Distance =
What is the distance from the point ( 7 , 4 , - 7

Evaluate the iterated integral. 0 6 0 8 ( x y ) d y d x
Evaluate the iterated integral. 0 6 0 8 ( x y ) d

Given the equation x ^ 2 + 3 x = y ^ 2 + y 6 , find dy / dx .

What is the value of [ 1 ( ) ] ddx [ f 1 ( x ) ] when = x = , given that ( ) = 2 + cos 2 f ( x ) = 2 x + cos 2 x and 1 ( ) = 2 f 1 ( ) = 2 ? Select one: a . 1 2 1 2 b . 1 4 1 4 c . 2 4 + 2 2 4 + 2 d . 2

x ^ 2 y ' ' + xy ' + 2 y = x ^ ( n + 2 ) how to solve this differential equation? There's no other information

Write the following equation in its equivalent logarithmic form. 1 2 Superscript 4 Baseline equals x

If f ( x ) = n = 0 n 1 n 2 x n and g ( x ) = n = 0 ( - 1 ) n n 1 n 2 x n , find the power series of 1 2 ( f ( x ) g ( x ) ) . Your answer cannot have ( - 1 ) n in it . n = 0
If f ( x ) = n = 0 n 1 n 2 x n and g ( x ) = n =

Evaluate the limit , if it exists. ( If an answer does not exi lim x - 3 x 2 3 x x 2 - 5 x - 2 4
Evaluate the limit , if it exists. ( If an answer

Find the absolute minimum and absolute maximum values of f on the given interval. f ( x ) = x 2 - 4 9 x 2 4 9 , [ - 4 9 , 4 9 ]
Find the absolute minimum and absolute maximum

t = 0 and t = 1 , respectivelyvec ( g ) ( t ) = ( 1 - 4 t , 1 - 4 t 3 , l n ( 3 t 4 + 4 ) ) Starting point: Ending point: Now compute the derivative o f that same vector - valued function. Answer: Now compute the starting and ending velocities for that same vector - valued function. Starting velocity:
t = 0 and t = 1 , respectivelyvec ( g ) ( t ) = (

The partial fraction decomponition of - 3 x 2 - 7 x 1 3 ( x - 1 ) ( x 2 - 3 x 3 ) can be written in the form of f ( z ) f ( z ) ( x - 1 ) g ( z ) ( - 3 - 9 x 3 ) , where f ( z ) g ( x ) =
The partial fraction decomponition of - 3 x 2 - 7

Determine the region i n which the function, f ( x , y ) = s i n ( x 2 + 3 y 2 ) x 2 + 3 y 2 , i s continuous. Function i s continuous everywhere except a t Function i s continuous everywhere
Determine the region i n which the function, f (

NEW RANDOMIZATION [ - / 1 Points ] 0 / 1 0 0 Submissions Used Suppose that f and g are functions that are differentiable at x = 1 and that f ( 1 ) = 2 , f ' ( 1 ) = - 1 , g ( 1 ) = - 2 , and g ' ( 1 ) = 3 . Find h ' ( 1 ) . h ( x ) = ( x 2 4 ) g ( x ) h ' ( 1 ) =
NEW RANDOMIZATION [ - / 1 Points ] 0 / 1 0 0

tuna, priced at $ 2 per can, and milk, priced at $ 1 per pint. What is Rafs alility - matining commpsion lousfle? M = 3 0 and T = 3 0 M = 4 0 and T = 2 5 M = 1 0 and T = 4 0 M = 1 5 and T = 6 5
tuna, priced at $ 2 per can, and milk, priced at

1 Solve the exact length of the curve x = 2 3 y 3 / 2 , 0 y 2 .

Find the shortest distance from the surface z = x 2 + y 2 to the surface x + y 2 z = 4 . DO NOT use the method of Lagrange Multipliers

The length of a rectangle is 2 in longer than its width. If the perimeter of the rectangle is 2 4 in , find its area.

Let f ( x , y ) = y 1 + x 2 y 2 . Find and simplify d e l f d e l x and d e l f d e l y . Then evaluate these derivatives at the point ( 1 , - 1 ) .
Let f ( x , y ) = y 1 + x 2 y 2 . Find and

( 1 point ) L { c o s } ( s ) = 0 e - s t c o s ( a t ) d t t = d v = d u = v = = | 0 - 0 | | u d v = du v = = - a 2 s 2 0 Notice that this last integral is the same as the integral we started with. Treat this like an equation and move the integral to the left hand side: e - s t c o s ( a t ) d t = 1 s Therefore e - t c o s ( a t ) d t =
( 1 point ) L { c o s } ( s ) = 0 e - s t c o s (

Use the second derivative test to answer: If f ( c ) exists, f ' ( c ) = 0 , and f ' ' ( c ) is positive, then ( c , f ( c ) ) is:
Use the second derivative test to answer: If f (

( a ) Show that any function of the form y = Asinh ( m x ) Bcosh ( m x ) satisfies the differential equation y ' ' = m 2 y . ( b ) Find y = y ( x ) such that y * * = 2 5 y , y ( 0 ) = - 8 , and y ' ( 0 ) = 1 5 . r ( x ) =
( a ) Show that any function of the form y =

Problem 1 1 of 5 0 Which of the following series of isoelectronic ions ( M g 2 , N 3 - , F - , S i 4 ) has the ionic radii in order of largest to smallest? Answer: A M g 2 > N 3 - > F - > S i 4 B M g 2 > S i 4 > F - > N 3 - c N 3 - > F - > S i 4 > M g 2 D N 3 - > F - > M g 2 > S i 4 E F - > N 3 - > S i 4 > M g 2
Problem 1 1 of 5 0 Which of the following series

Determine the set of points at which the function is continuous.F ( x , y ) = D = ( x , y ) | x 2 y ? - x 2 - y 2

Simplify the given expression. Express answer with positive exponerce. ( 9 8 x 4 y 6 ) 1 4 5 x - 3 y 8 A ) 9 2 x 4 y 1 3 2 5 B ) 9 2 x 4 5 y 1 3 2 C ) 9 x 4 5 y 1 3 2 D ) 9 2 y 1 3 2 5 x 4
Simplify the given expression. Express answer

what i s l n ( 1 5 x 5 ) x d x ?

A company has profits of \ ( \ $ 3 5 , 0 0 0 \ ) this year and expects profits to decrease by \ ( \ $ 1 5 0 0 \ ) dollars per year over the next 9 years. If the profits will be continuously invested in an account bearing \ ( 6 . 9 \ % \ ) APR compounded continuously, what is the 9 - year present value of this income stream? Round your answer to
A company has profits of \ ( \ $ 3 5 , 0 0 0 \ )

A company has profits of $ 3 3 4 , 0 0 0 this year and expects profits to decrease by 4 % per year over the next 1 1 years. If the profits will be continuously invested in an account bearing 6 . 1 % APR compounded continuously, what is the 1 1 - year future value of this income stream? Round your answer to two decimal places. Do not include units.
A company has profits of $ 3 3 4 , 0 0 0 this

Find a power series representation for the function. ( Give your g ( x ) = x 8 l n ( 1 x ) g ( x ) = n = 1 Evaluate the indefinite integral as a power series. What is the radius of convergence R ? R =
Find a power series representation for the

1 . [ 8 points ] Determine whether the following statements are true or false. a . TRUE or FALSE: If ( , ) = 2 + 2 1 0 , then ( , ) = 2 + 2 . b . TRUE or FALSE: Because the gradient gives the direction of maximum increase of a function, the gradient is always positive. c . TRUE or FALSE: The gradient of ( , , ) = 1 + has four components. d . TRUE

Suppose that the population \ ( P ( t ) \ ) of a country satisfies the differential equation \ ( \ frac { d P } { d t } = k P ( 9 0 0 - P ) \ ) with \ ( k \ ) constant. Its population in 1 9 6 0 was 3 0 0 million and was then growing at the rate of 1 million per year. Predict this country's population for the year 2 0 1 0 . This country's
Suppose that the population \ ( P ( t ) \ ) of a

Find a n equation for the contour o f f ( x , y ) = 2 x 2 y + 1 5 x + 1 5 that goes through the point ( 3 , 2 ) . Equation:
Find a n equation for the contour o f f ( x , y )

Set u p , but d o not evaluate, integral ( s ) for the area o f the shaded region o f Tschirnhausen's cubic, which i s defined b y y 2 = x 2 ( x + 3 ) . Hint: Solving for y , one obtains y = + - x 2 ( x + 3 ) 2 . Consider these a s your two functions and compare t o the picture.
Set u p , but d o not evaluate, integral ( s )

2 5 1 p t s 1 2 7 0 0 Resources Question 3 of 2 7 Find a formula a n for the n - th term of the following sequence. Assume the series begins at n = 1 . 1 1 , - 1 8 , 1 2 7 , dots ( Use symbolic notation and fractions where needed. ) a n = Find a formula b n for the n - th term of the following sequence. Assume the series begins at n = 1 . 3 6 , 4
2 5 1 p t s 1 2 7 0 0 Resources Question 3 of 2 7

Fabric Asymmetrical.. ( P ) PAVOI Best Sellers | 1 4 K . . . Exam 1 - Mandatory Exam 1 - N ry 9 of 9 This test: 1 0 0 po This question: 1 0 Determine the following limit . lim x 3 5 x 3 5 x 2 - 5 x 2 8 x 3 x 2 3 x 5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A . lim x 3 5 x 3 5 x 2 - 5 x 2 8
Fabric Asymmetrical.. ( P ) PAVOI Best Sellers |

The balance A ( in dollars ) in a savings account is given by A = 5 0 0 0 e 0 . 0 9 t , wher ( a ) t = 1 year $ per year ( b ) t = 1 0 years $ per year ( c ) t = 5 0 years $ per year Need Help?
The balance A ( in dollars ) in a savings account

For the series below calculate find the rumber of terms n that must be added in onder to find the sum bo the indicated accuracy. n = 1 ( ( - 1 ) n 5 n n ) | enor | 0 . 0 1 n =
For the series below calculate find the rumber of

For the function f ( x ) given below, evaluate lim x f ( x ) and lim x - f ( x ) . f ( x ) = - 3 x 1 4 x 2 - 3 2

Use the root test to find the radius of convergence for n = 1 ( n - 1 5 n 9 ) n x n
Use the root test to find the radius of

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