Calculus Questions

Given f x 7 x and g x 6x find the following expressions a fog 4 b gof 2 c fof 1 d gog 0 198 a fog 4 14 6 Type an exact answer using radicals as needed Simplify your answer b gof 2 Type an exact answer using radicals as needed Simplify your answer

0x45x 4 2 C

Given f x 7 x and g x 6x find the following expressions a fog 4 b gof 2 c fof 1 d gog 0 a fog 4 Type an exact answer using radicals as needed Simplify your answer

a x 2x 11x 12 0

Given f x 5 x and g x 3x find the following expressions a fog 4 b gof 2 c fof 1 d gog 0

1 Determine whether the given functions are linear or nonlinear If it is linear determine the slope a x f x 1 5 0 2 1 2 4 3 1 S 7 b x g x 2 28 1 7 0 1 5 2 155

Choose the correct pair of functions OA f x x g x O B f x x g x 3x 8 X 8 3 OC X 8 3 f x g x x O D f x 3x 8 g x x

For f x x and g x x find fog x and gof x Then determine whether fog x gof x What is fog x fog x x What is gof x 0 gof x

For f x 8x and g x x find fog x and gof x Then determine whether fog x gof x What is fog x fog x ww

For f x x and g x x find fog x and gof x Then determine whether fog x gof x What is fog x fog x

g x 3 2 4 x 1 2

j x 5x 2x 8

i x 6x 11x 6

Between 8 30 and 9 30 a m cars drive through the Lincoln Tunnel at a rate of 12 cars per hour 0 2 per minute The formula below can be used to determine the probability P that a car will arrive within t minutes of 8 30 a m Determine the number of minutes needed for the probability to be 0 6 P 3 9 000 165 P t 1 e 0 2 OR ad of bespieg

2X

ople there are at least two people who have the same birthday the same month and day of called the birthday problem is to find the probability that in a group of the year Assume a person is as likely to be born on one day as another

8 cos x 1 n 0 1 n x n 2n

entify the property of a gas that is measured in each of the llowing measurements lo Part A 425 K pressure amount of gas O volume temperature Submit Request Answer Part B 010 1 00 atm temperature volume pressure amount of gas

Let co ci x a c x a cn a be the Taylor series of the function f x x sin x For a 0 determine the value of c3

Find the Maclaurin polynomials of orders n 0 1 2 3 and 4 and then find the nth Maclaurin polynomials for the function in sigma notation Enter the Maclaurin polynomials below for Po x P1 x P2 x P3 x P4 x Pn x m 0

Use cylindrical coordinates to find the volume of the region bounded by the plane z 0 and 2 the hyperboloid z 2 x y The volume is Type an exact answer using as needed www ZL

For the following function find the Taylor series centered at 7 and then give the first 5 nonzero terms of the Taylor series and the open interval of convergence f x e8e f 2 20 71 0 f x 0 0 0 0 0 The open interval of convergence is Give your answer in interval notation

1 point The function f x is approximated near x 0 by the second degree Taylor polynomia P x 3 3x 8x Give values f 0 0 f 0

If y k 1 x 3 then y 0 k 0

Find the second degree Taylor polynomial for f x 5x 9x 2 about x 0 P x What do you notice about your polynomial

This question 1 point s possib A full time worker aged 25 invests 500 a month in a fund which has an average yearly return of 8 4 compounded monthly a The worker wants to estimate what they will have for retirement when they are 60 years old if the rate stays constant Assume monthly compounding b If the worker makes no further deposits and makes no withdrawals after age 60 how much will they have for retirement at age 71 a How much money will the worker have in their fund when they are 60 years old The worker will have in their fund when they are 60 years old Round to the nearest cent as needed b If the worker makes no further deposits and makes no withdrawals after age 60 how much will they have for retirement at age 71 The worker will have in their fund Round to the nearest cent as needed

ritz Benjamin buys a car costing 15500 He agrees to make payments at the end of each monthly period for 5 years He pays 4 8 interest compounded monthly What is the amount of ach payment Find the total amount of interest Fritz will pay Fritz s monthly payment is Round to the nearest cent Fritz will pay a total of Round to the nearest cent in interes

54 4 3 OF 7 wh 5 O 10 3 4 5 6 7 8 O The graph of a function y f x is shown Make a sketch of the antiderivative F given that Fis continuous and F 0 1 3

Find the monthly house payments necessary to amortize a 4 8 loan of 205 700 over 15 years The payment size is Round to the nearest cent

A man deposits 17 000 at the beginning of each year for 16 years in an account paying 7 compounded annually He then puts the total amount on deposit in another account paying 9 compounded semiannually for another 14 years Find the final amount on deposit after the entire 30 year period He will have a final amount of after the entire 30 year period Simplify your answer Round to the nearest cent as needed C

Find the final amount in the following retirement account in which the rate of return on the account and the regular contribution change over time 212 per month invested at 4 compounded monthly for 3 years then 799 per month invested at 6 compounded monthly for 3 years What is the amount in the account after 6 years Round to the nearest dollar as needed

order to accumulate enough money for a down payment on a house a couple deposits 790 per month into an account paying 3 compounded monthly If payments are made at the end of ch period how much money will be in the account in 4 years That is the amount in the account after 4 years Round to the nearest rent as needed

Suppose that f x and g x are given by the power series f x 7 6x 4x 5x and g x 6 9x 5x 2x By multiplying power series find the first few terms of the series for the product h x f x g x co C x c x 3x Co 11 C1 11 C2

A woman deposits 11 000 at the end of each year for 6 years in an account paying 7 interest compounded annually a Find the final amount she will have on deposit b Her brother in law works in a bank that pays 6 compounded annually If she deposits money in this bank instead of the other one how much will she have in her account c How much would she lose over 6 years by using her brother in law s bank a She will have a total of on deposit Simplify your answer Round to the nearest cent as needed b She will have a total of on deposit in her brother in law s bank Simplify your answer Round to the nearest cent as needed c She would lose Simplify your answer over 6 years by using her brother in law s bank Round to the nearest cent as needed

5 Let A x f t dt with f x shown in the graph below 4 3 P 1 2 3 4 5 a sim 3 question You can retry this question below Add Work 5 At what a value s does A x have a local max x 2 9 Use commas to separate multiple values At what a value s does A x have a local min a value This is not a decimal or integer value Use commas to separate multiple values Restrict your responses to values 0 x 6 Q 0 9 4 9 X X This is not a decimal or integer

Consider the function f t 8 sec x tan x 6 cos x 15 sin x Let F x be the antiderivative of f x with F 0 0 Then F x 4 sec x 6 sin x 15 cos x 19 X

The graph below shows the constant function y c t 8 7 6 5 4 3 2 8 7 Answer 5 A 3 2 1 1 2 3 45 5 6 18 1 2 3 4 5 6 7 8 A new function w is defined as an integral w x c t dt 1 What is the value of w 3 We know that w is an antiderivative of c What is the formula for w

Consider the graph of f N 1 2 3 4 5 6 7 8 P10 The shaded region over 6 9 has an area of 33 and the following definite integrals 0 f x dx f x dx f x dx If a f x 9 dx f x 9 dx 9 f x dz 183 Use this information to eval

Let A x 5 4 3 12 2 3 4 5 f t dt with f x shown in the graph below 3 5 At what a value s does A x have a local max x x Use commas to separate multiple values At what a value s does A x have a local min x Use commas to separate multiple values Restrict your responses to values 0 x 6 Ta

Evaluate the following integral in cylindrical coordinates 3 9 x x y 24 S 0 0 0 9 x x y 1 2 x y dz dy dx x y 1 dz dy dx 0 0 0 Type an exact answer using as needed

Find a function F x such that F x 4x 7 and F 2 20 F x

2 While in the barrel of a tennis ball machine the acceleration a in m s of a ball is

3 A motorcycle accelerates at a constant rate from 0 km h to 105 km h in 18 0 seconds

Find the fourth partial sum and the sum of the infinite series 1 2 10 i 1 a the fourth partial sum b the sum of the infinite series

Use sigma notation to write the sum 4 4 5 2 5 3 i 1 4 5 1 4 5 15

Write an expression for the apparent nth term an of the sequence Assume that n begins with 1 6 7 8 9 10 3 7 11 15 19 an

Write an expression for the apparent nth term an of the sequence Assume that n begins with 1 1 16 an 11 1 1 F 2 4 8 I

Match the sequence with its graph 4n n 1 an 10 8 6 4 2 an 10 8 6 4 N 2 4 2 4 8 10 6 8 10 an 10 8 16 4 an 10 8 4 2 2 4 6 8 6 8 10

Find the sum 4 j 1 2 j

Simplify the factorial expression n 3 n