Calculus Questions

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Consider the indefinite integral u ex 5 and e z e 5 This can be transformed into a basic integral by letting du e X 7 U dx Performing the substitution yields the integral n du S Integrating yields the result da

Use the Definition to find an expression for the area under the graph of f as a limit Do not evaluate the limit f x x 1 2x 6 x 8 lim 1248 3 Morrage instructor

Oil leaked from a tank at a rate of r t liters per hour The rate decreased as time passed and values of the rate at two hour time intervals are shown in the table Find lower and upper estimates for the total amount of oil that leaked out V V L lower estimate Question Help L upper estimate t h 0 2 4 6 8 10 r t L h 8 8 7 9 6 8 6 2 5 7 5 1

Consider the function f t 5 sec t 4t Let F t be the antiderivative of f t with F 0 0 32 Then F 2 5 tan 2 OF

What is one concern with the use of genetically engineered herbicide tolerant crops transfer of herbicide resistance to weeds O potential allergic reactions O Decreased Yield expense of using herbicides

The function f x 7x 9x has one local minimum and one local maximum Algebraically use the derivative to answer the questions Leave answers in 4 decimal places when appropriate this function has a local maximum at with value and a local minimum at x with value

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function tanz S 6t t dt

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function 5 7 1 t 7 g x Question Help dt Video Message instructor

Use implicit differentiation to determine dy dx 322 cos y dy da given the equation x y siny

If f 1 10 f is continuous and f 5 x d 17 what is the value of f 5

Find the sum 31 16 10 2 k 0 X

Write the sum using sigma notation 4 5 6 15 15 k 4

Find the sum 6 k 2 24 1

Divide using long division 3 8m 51m2 27m 56 m 7 OA m 6m 7 2 OB m 5m 8 2 OC 8m 5m 8 OD 8m 5m 8

The logistic growth function f t OA 353 butterflies OB 253 butterflies OC 5 040 butterflies OD 153 butterflies 360 1 8e 0 211 describes the population of a species of butterflies t months after they are introduced to a non threatening habitat How many butterflies are expected in the habitat after 14 months Round to nearest whole numb

Write the first five terms of the arithmetic sequence a 12 d 2 OA 12 10 8 6 4 OB 16 13 10 7 4 OC 0 12 10 8 6 D 12 10 8 6 4

Write the first five terms of the arithmetic sequence a 7 d 2 OA 7 8 9 10 11 OB 9 11 13 15 17 OC 0 7 9 11 13 OD 7 9 11 13 15

Is the function a polynomial function f x O O 4 X Yes No 9x 9

Find the slant asymptote if any of the graph of the rational function g x x 3 2 X 36 A y x OB y x 3 OC y x 36 OD no slant asymptote

A salesperson gets a commission of 1 200 for the first 10 000 of sales and then 600 for each additional 10 000 or partial of sales Let S x represent the commission on x dollars of sales Find the value of S 95 0 OA 5 700 O B 6 300 O C 6 900 OD 6 600

Find and simplify the difference quotient f x 6 OA O OB 1 OC 1 OD 6 12 h f x h f x h h 0 for the given function

Find the sum of the infinite geometric series if it exists 8 0 1 1 i 1 OA OB O C OD 80 11 80 9 80 80 9

Find the domain of the rational function f x X 2 x 2 25 OA xx 5 x 5 OB xx0 x 25 OC all real numbers OD xx 5 x 5 x 2

Given functions f and g find f g f x 6x 2 g x 9x 7 OA 3x 5 OB 15x 9 OC 3x 9 OD 3x 5

Write the first five terms of the arithmetic sequence O A OB O C O D 5 7 d 5 SIG 5 7 5 7 5 7 7 7 7 2 7 mit 3 1 C 113 10 15 20 7 7 7 7 7 www 7 11 www BE 11 3 7 7 HON 11 7 7 21 22 15 7

Use properties of logarithms to condense the logarithmic expression Write the expression as a single logarithm whose coefficient is 1 Where possible evaluate logarithmic expressions log a9 logar 4 log ap OA log a 4qp r OB loga ap OD log 4 qp OC log an q

Use the formula for the general term the nth term of a geometric sequence to find ag with the given first term a 6 and common ratio r 2 OA 1 536 OB 1 532 OC 22 OD 3 072

Approximate the number using a calculator Round your answer to three decimal places 2 6 OA 6 000 OB 5 462 OC 4 899 OD 32 000

List the intervals on which the function is increasing the intervals on which it is decreasing and the location of all local extrema Ay A 2 Q List the open interval s on which the function is increasing Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function is increasing on the interval s Type your answer in interval notation Use a comma to separate answers as needed OB The function is never increasing List the open interval s on which the function is decreasing Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function is decreasing on the interval s Type your answer in interval notation Use a comma to separate answers as needed OB The function is never decreasing Identify any local extrema Select the correct answer below and if necessary fill in any answer box es within your choice OA There is no local maximum and the local minimum minima occur s at x Use a comma to separate answers as needed OB There is no local minimum and the local maximum maxima occur s at x Use a comma to separate answers as needed OC There is are local maximum maxima at x at x Use a comma to separate answers as needed OD The function has no local extrema and there is are local minimum minima

Find the zero of the function shown below f x 2 2x 3x 4 8 x 4 O A OB 12 5 5 C 4 OD 4

Find the location of the absolute maximum and absolute minimum of the function on the interval 6 0 The absolute maximum occurs at x Use a comma to separate answers as needed The absolute minimum occurs at x Use a comma to separate answers as needed Af x A

Use the graph of the function f to find lim f x and X 8 lim f x X 00 Select the correct choice below and fill in any answer boxes in your choice OA lim f x X OB The limit does not exist and is not co or 0 Select the correct choice below and fill in any answer boxes in your choice OA lim f x X 00 OB The limit does not exist and is not oo or 00 10 BB

8 Find the radius of convergence and interval of convergence of n 1 xn n5n

11 Find dx dt dy dt and dy dx where x 2et y t cost do

2 Find cos 0 sin 0 de moyur in to enroldeig nivollol edy to lis od ar 10 mq dto vas mol glid on wison 1 I talt bartition 1 tuonsob zid gaingie

a Find the third degree Maclaurin polynomial for f x 6 Solve b Use your answer above to approximate the cos 1 sin 1

5 Solve y 3x y y 0 1

5 The surface area of a cube is equal to the sum of the areas of each of its six square faces The formula to find the surface area of a cube is A 6x where x is the side length of one of the square faces Jack has two cubes that he needs to paint One of them has a side length of 2 inches and one has a side length of 1 5 inches How many square inches does he need to paint

Find 32 3 Find 3x x 1 dx

9 Find an equation tangent to the curve at the point when t 4 and at 13 y 5t bail

Solve y y 1 Gal

1 Find x e dx

3 Find 3x x 1 da

11 Find dx dt dy dt and dy dx where x 2et y t cost adl of caston PAUZ

2 Find I cos 0 sin 0 de 10 9 19 slingbaon do pilog off mot sa om my moldog nivellot si to lis od anoitourten evinson 1 1 tl dusze eld amplas haditios I tomusob eids gningiz va ogbolT ala orozite of qlod obivorq ton bib S bus ou widton hib bus avdellve od ni vjes

Find the des using the geometric distribution the Poisson distribution or the binomial distribution I hen determine if the events are unusual If convenient use the appropriate probability table or technology to find the The mean number of births per minute in a country in a recent year was about seven Find the probability that the number of births in any given minute is a exactly four b at least four and c more than four sled prc a P exactly four Round to four decimal places as needed b P at least four Round to four decimal places as needed c P more than four Round to four decimal places as needed Which of the events are unusual Select all that apply A The event in part a is unusual B The event in part b is unusual C The event in part c is unusual D None of the events are unusual

Assignment 3 5 points Consider the following linear optimization problem min I1 312 s t 221 213 12 13 313 12 21 21 T2 13 I1 I4 TA 14 13 24 8220 C4 a Reformulate the problem in standard form b Introduce slack variables and give the dictionary with the slack variables in the basis Does this dicti

2 The graph for f has a domain of 1 5 and range of 4 10 Let g x Find the domain and range of g x f x 3 6 4 points

Use absolute value on a graphing calculator to find the area bounded by the graphs of the equations over the given interval y exy 0 11x 0 41 2 x 2 The area is Round to three cubic units units d