Calculus Questions

Differentiate the function f x f x sin 7 In x

The number of users on a website has grown exponentially since its launch After 1 month there were 120 users After 4 months there were 960 users Find the exponential function that models the number of users x months after the website was launched Write your answer in the form f x a b Provide your answer below

Question A sample of bacteria is being eradicated by an experimental procedure The population is following a pattern of exponential decay and approaching a population of O If the sample begins with 500 bacteria and after 11 minutes there are 200 bacteria after how many minutes will there be 50 bacteria remaining Round your answer to the nearest whole number and do not include units

A radioactive substance has a continuous decay rate of 0 044 per hour How many grams of a 100 gram sample will remain radioactive after 2 hours Round the answer to the nearest tenth of a gram and do not include the unit in your answer If necessary include a leading 0 with any decimals less than 1 For example 0 4 instead of 14

The total amount paid on a 35 year loan was 98 000 If the interest rate was 4 1 and compounded monthly what w the principal Round your answer to the nearest dollar

2 Simplify the following 2sin2x sinx 1 sin2x sinx

1 Evaluate the following 2 a tan cos b sin cos Crat sin

4 Find all solutions to the trigonometric equation tan 0 sec 0 1

Solve log 5 x 4 log 9 4x Round your answer to the nearest tenth Do not include x in your answer If necessary include a leading 0 before the decimal point For example 0 5 instead of 5

Use the one to one property of logarithms to solve for x Do not include x in your answer log 2x 1 log 3x 5

Solve the following equation for x In 3x 5 6 Round your final answer to 4 decimal places and do not include x in your answer

3 Use Simpson s Rule in Maple with n 32 to approximate the integral Vsin x dx Take a picture of your Maple output and upload it to Moodle as a pdf together with your worksheet solutions

Solve the following equation for x Provide your answer below log 6x 84 log 3 2

1 point Give a vector parametric equation for the line through the point 1 2 that is perpendicular to the line 3 5t 1 t L t

Q2 Find a scalar potential field for F i j k x y z Explain why this potential field cannot be used to evaluate the line integral of F along r t ti tj f k 1 t 1 Total for Question 2 5 marks

Find the indicated limit Note that l H pital s rule does not apply to every problem and some problems will require more than one application of l H pital s rule Use o or co when appropriate 2e x lim x In 1 7ex Select the correct choice below and if necessary fill in the answer box to complete your choice 2e x lim OA x In 1 7e 11 11 Type an exact answer in simplified form B The limit does not exist

zilldiffeqmodap11 7 4 009 EP consider the following initial value problem y y tsin t y 0 0

A T shirt manufacturer is planning to expand its workforce It estimates that the number of T shirts produced by hiring x new workers is given by T x 0 25x 3x 0 x 9 When is the rate of change of T shirt production increasing and when is it decreasing What is the point of diminishing returns and the maximum rate of change for T shirt production Graph T and T on the same coordinate system The rate of change of T shirt production is increasing on Type your answer in interval notation

Find the critical numbers the intervals on which f x is increasing the intervals on which f x is decreasing and the local extrema Do not graph f x 3x 147 X Select the correct choice below and if necessary fill in the answer box to complete your choice A The critical number s is are 7 7 Type integers or simplified fractions Use a comma to separate answers as needed OB The function has no critical numbers Select the correct choice below and if necessary fill in the answer box to complete your choice A The function is increasing on 7 x x 7 Type your answer in interval notation Type integers or simplified fractions Use a comma to separate answers as needed

ind f x 1 x x 3 4 2 f x 8 x 3 x 3x 3 2

Use the graph of f x to discuss the graph of y f x Organize your conclusions in a table and sketch a possible graph of y f x U D me function is never decreasing Af x 10 10 Q G Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function f is increasing on the subinterval s Type your answer using interval notation Use a comma to separate answers as needed B The function f is never increasing

Solve the equation for a where x is in radians State the exact solutions if any that lie in the interval 0 2 If the equation has no solutions respond with DNE 4 4 sec x sec x sec x 3 3 Separate multiple solutions with a comma

Find the magnitude of the complex number z 8 6i 2

Solve 9e7x 17 Round your answer to the nearest tenth Do not include x in your answer If necessary include a leading 0 with an decimals less than 1 For example 0 5 instead of 5

find the derivative of the given function y x e 3x y Ctype an exact unsuer

0 Evaluate the definite integral action 5 12 Cinx dx x

Solve 11e 21 Round your answer to the nearest tenth Do not include x in your answer If necessary include a leading 0 with am decimals less than 1 For example 0 5 instead of 5

Find the x and y coordinates of all inflection points 9 5 f x 2x 4 What is are the inflection point s Select the correct choice below and if necessary fill in the answer box to complete your choi A The inflection point s is are 72 Type an ordered pair Use comma to separate answers as needed OB There are no inflection points

Find the intervals on which the graph of f is concave upward the intervals on which the graph of f is concave downward and the inflection points f x x 9x 13x 7 For what interval s of x is the graph of f concave upward Select the correct choice below and if necessary fill in the answer box to complete your choice A Type your answer in interval notation Type an exact answer Use a comma to separate answers as needed OB The graph is never concave upward

Find the indicated derivative for the function h x for h x 7x7 6x8 h x

6 Determine whether or not the function is continous for the given value of X FCX x 4 X 2 x 0 x 2 x 2 Is the function continous at x 0 select the Correct choice below and if recensing fill in the ander bety OA Yes the point is defined limf x exists and lim F x OB NO the function is not continous at X 0 simptly you Is the function continous cut X 23 OA Yes the point is defined lim Fax exists and lim x XCX 277 B No the function is continous at X 20 not Is the function continous at x 27 watchist xon 950 OA Yes the point is defined lim fox exist and lim F x X 9 2 OB No The Function is not Continuous at X 2

Solve 6 3 8 Enter an exact answer or round your answer to the nearest tenth Do not include x in your answer

is the knoth which is concave upward or concave d ownward and find the location of a any points of inflection F x x 4x 8x 4 MON correcta select the below and fill in the blanks to complete your choice Type your answer in interval notation use a comma seperale answer answer as needed Use integers or fraction numbers in the expression x to for 57 any JK Dalyvia A The function is concave upward on and concave downund on The function is concave downward on They are no intervals on which the function is concave upward The function is concave upward on There are no b intervals on which the function is concave down word Select the correct choice bellow and if necessary fill in the ansung box A The Function has point s of inflection aut ctype an orded pair Use a Comma to sepeate as needed LAVS a B There is no point of inflection 102

Write log 3x in expanded form

bstitution integral Sx 2x 5 dx 28 5

Solve 9x 5 6 Enter an exact answer or round your answer to the nearest tenth Do not include x in your answer

Write In 8t in expanded form Note When entering natural log in your answer enter lowercase LN as In There is no natural log button on the Alta keyboard

27 find all critial for the following function Then use the second derivative test on each critical number to determine whether it leads to a local maximum o minimum F x 2x 3x 12x 2 What is the second deles derivatie of x F x find all critical a local Correct choice bellow numbers and determine whether they lead maximum or minimum select the A The critical number s is a x there is a local maximum at X There is no local in These is The critical number S is are Xz no local maximum There is a local minimumatx The critical number s is are x D There is no local maxima and no local minimam I there are no criticul numbers The critical numbers s is are x These is a local maximum at X There is a local minimum aut X use a comma to separate ansur as needed

Write the expanded form of log x cwor below

13 Determine the location of each local extremum of the function 13 2 FCX x 12x 45x 2 what is are the local minimum minima select the all Correct choice below and if necessary fill in the answerbet A The local minimum minima is are at x 1 use a comma to separate ansuer as needed Type integess or simpired fruction B The function has no local a what is are the local maximm maxima select the correct choice 8 cixs tun wala A The local maximum maxima is are use a comma minimum atx to seperate ansug as needed rype or simplifed fraktion b saktion 779 211 6309900 integers B The Function has has no I local maximum

9 Use the definite integral to find the area between the x axis and FCX over the indicated interval Check firs to see if the graph crosses the x axis interval in the given F x 4 1 5 The area between the x axis and F x is simplity your answer Type integar fraction an m or an improper 507 pxal

Suppoes He demand function for x thousand of a certain item is p 130720 where x 1 and pis in dollars d find the marginal revenue b find the revenue from the next thousand a demand of 8000 x 8 The revenue from the next thousand items when intens at Crype an integer or decimal sounded to two decimal places as needed

find the derivative of the function 9 5x 8 7x 1 The derivative is y S CA 29 StXV is y los Jesen hibao wolker

Sketch the region enclosed by y 4x and y 5x Find the area of the region

21 use the properties of limits to find the indicated limit lim x 7x 3 X 8 x 3x 4 option A O B 3 Trokre of Gay Tub

30 use a calculator to estimate the limit mique 5X on word not lim X 0 option A 0 0 0 2015 02 ond B D Does not exist and is not or 00 mumxan Lou GNT A

Evaluate the integral 7 zett utett dt

5 find the equation of the tangent line to the stroph offCX at the given point x 10x 5 at 2 5 equation of the tangent line to the graph of f x the given point is

23 find the followi llowing F u iF F X 7 x X option A t B 17 16 GEM B new a D H B 7

the given limit 22 use the properties of limits to find nove lim kino 7x 7x 3 type an integer or a simplified fraction 23 8x5