Calculus Questions

nd the derivative x f x ex cosh x

Write name date and period Explain all answers including Multiple Choice Each problem is worth 4 points 1 The number of shoppers in a shopping mall t hours after it opens is given by S t The number of store cle needed to attend to s shoppers is given by C s Interpret the statement C S 3 11 in the context of this problem

Find the numerical value of each expression Round your answers to five decimal a cosh In 9 b cosh 9

Prove the identity Recall sinh a b sinh a cosh b cosh a sinh sinh 2x 2 sinh x cosh x sinh 2x sinh x sinh x 2 sinh x cosh x cosh x sinh x

5 2 The new cookbook you just got gives all the oven temperatures in degrees Celsius but your oven uses degrees Fahrenheit Additionally your oven runs hot and you always have to decrease the prescribed temperature by 15 F Write an expression using a composition of functions that will determine how high you have to preheat your oven when a recipe from your new cookbook calls for a temperature of t C Hint C F 32 and C 32 are the equations to convert between degrees Celsius C and degrees Fahrenheit F 9 9 F C

Use the chain rule to find the derivative of 8 7x 9x Type your answer without fractional or negative exponents Use sqrt x for x

Find dy da dy da 11 for y Question Help In 3x 10 6e5t Video Written Exar

9 The graph of a function f is shown on the interval 7 5 Let g x 5x 8 a Find f g 1 b Find g f 3 O M 3 2 1 4 8 7 6 5 4 3 2 1 0 1 2 3 5 61 1 2 3 4 5 6

8 Let f x x 2 and g x A f g 3 B g f 11 C g 2 D f g 5 4 2x 6 Which of the following is defined

6 Given the functions f x x and g x x 2 which of the following graphs could represent y g f x A 64 5 O 2 8 9 10 11 E B D 3 10 0 10 11 10 TI

4 Let f x x 1 and g x 3x 7 a Find f g 2 b Write an expression for f g x c Find g f 2 d Write an expression for g f x

5 If h f x 3 x 7 find a possible expression for h x and f x

3 A table of selected values is given for the functions f and g The domain of both functions is all real numbers f x x g x 5 11 11 3 8 0 6 4 3 8 6 XC 3 3 5 2 5 1 0 2 4 7 Find f g 4

Find the following limits 5 3 4 x 3x 2 a lim xx 5 4 x x 3x 2 b lim

Evaluate the limit using L Hospital s rule if necessary sin 8x lim 0 sin 7x cos x cos x Question Help Video X syntax incomplete an retr

Let f x H 3e 2 1 e The graph of f is given below Use the graph of f to determine the given limits Enter DNE if a limit fails to exist except in case of an infinite limit If an infinite limit exists enter or as appropriate 5 4 1 5 4 3 2 1 lim f x I lim f x SO 2 2 2 3 4 5 I 2 3 4 5

Use the Intermediate Value Theorem to show that the following function has a zero in the given interval Approximate the zero correct to two decimal plac f x 3x 9x 9x 9 4 3 Select the correct choice below and if necessary fill in the answer box to complete your choice 0 and f 3 0 OA The polynomial has a real zero on the given interval because f 4 Type integers or decimals OB The polynomial has a real zero on the given interval because f 4 0 and f 3 Type integers or decimals 0 OC The polynomial has a real zero on the given interval because f 4 and f 3 are both positive OD The polynomial has a real zero on the given interval because f 4 and f 3 are both negative

2 Suppose f x 3x x 2 x 7 Determine where the tangent line to y f x is horizonte

204 Find dy dr if y e6x 2r

201 Find f x if f x H T 32

Use the rational zeros theorem to list the potential rational zeros of the polynomial function Do not attempt to find the zeros 11 8 f x 2x 1 x 2x 52 Find the potential rational zeros Choose the correct answer below OA 1 1 2 2 4 4 13 13 26 26 52 52 OB 1 1 2 2 4 4 13 13 52 52 OC 1 1 2 2 4 4 13 13 52 52 1 1 2 2 OD 1 1 2 2 4 4 13 13 26 26 52 52 1 1 2 2 1 22 1 52 52 1 1 13 13 2 2 22 1 1 52 52 31 1 1 32 52 52 1 1 13 13 2 2 22

3 f x x 12x 34x 16 to facto11 The real zero s of f is are 8 2 2 2 2 Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Use a comma to separate answ Factor f f x Factor completely Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression

qual x 2x 8x 32x 128 0 system Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the once OB The solution set is

zeros theorem to list the potential rational zeros of the polynomial function Do noteltempt to find the z f x x5 8x 8x 9x 5 Find the potential rational zeros Choose the correct answer below OA 5 5 11 5 5 1 1 OB 1 1 5 5 11 OC 1 1 5 5 5 5 OD 1 1 5 5

A particle moves along the x axis in such a way that its position at time t is given x 3t4 16t 24t2 for 5 t 5 a Determine the velocity and acceleration of the particle at time t b At what values of t is the particle at rest c At what values of t does the particle change direction d What is the velocity when the acceleration is first zero

10x 13x 22 f x x 10 The real zero s of f is are Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed

3 Let f x x 51 13x 61 What is the value of f 1 Be sure to show your work

2 Given the function defined by f x x x 4x 4 Find the zeros off a b Write an equation of the line tangent to the graph off at x 1 The point a b is on the graph off and the line tangent to the graph at a b passes through the point 0 8 which is not on the graph off Find the values of a c and b

A particle moves along the x axis in such a way that its position at time t is given 4 by x 3t4 16t 24t for 5 t 5 a Determine the velocity and acceleration of the particle at time t

the remainder theorem to find the remainder when f x is divided by x 2 Then use the factor theorem to determine whether x 2 is a factor of f x f x 3x 2x 10x 10 The remainder is 6 Is x 2 a factor of f x 3x 2x 10x 10 Yes No 09 1 of Points 0 of 1

Use the remainder theorem to find the remainder when f x is divided by x 2 Then use the factor theorem to determine whether x 2 is a factor of f x f x 3x 2x 10x 10 The remainder is

Given the function defined by f x x x 4x 4 Find the zeros off Write an equation of the line tangent to the graph of fat x 1 a b

Complete the sentence below If f is a polynomial function and x 5 is a factor of f then f 5 If f is a polynomial function and x 5 is a factor of f then f 5

3 4 Find the equation of the tangent line to the curve f x x 2x 6 at the point 2 6 4 marks

Show all your work Clearly indicate the methods used as you will be graded on the correctness of your method as well as your accuracy of your final answer Each question is worth 10 points Please keep your work as neat as possible so I may easily grade and return the problem set quickly 1 The line x c where c 0 intersects the cubic y 2x 3x 9 at a point P and the parabola y 4x 4x 5 at point Q a If a line tangent to the cubic at point P is parallel to the line tangent to the parabola at point O find the value of c where c 0

Solve the equation in the complex number system x 10x 50 0 What is the solution set Use a comma to separate answers as needed

Write the expression in the standard form a bi 7 5 6i 7 5 6i Simplify your answer

Write the expression in the standard form a bi 9 4i 2 i 9 4i 2 i Simplify your answer

Multiply 5 6 4i 5 6 4i Type your answer in the form a bi

Write the expression in the standard form a bi 5 3i 5 7i 5 3i 5 7 Simplify your answer

A GPCRs activate G proteins by reducing the strength of GDP binding allowing GDP to dissociate and GTP which is present in much higher concentrations to bind What would happen if the affinity of Ga for GDP were reduced but the affinity for GTP remained unaffected Explain your reasoning make sure to explain the effect on amount of pathway signaling as compared to non mutated Ga and then why

To find the derivative of y 3x 6x 4 would require the chain rule What functions f x and g use to find y if y f g x

106 Find the derivative of f x ln x5 6x

104 If h x 91 f x find f x

Which of the following is an equivalent expression to f g x g f x x g x f x g x f g x

4 1 Points DETAILS LARPRECALCRMRP7 5 1 036 Use the fundamental identities to simplify the expression Use the table feature of a graphing utility to check your result numerically cos x 1 tan x Need Help Read It Submit Answer 5 1 Points DETAILS Factor the expression and use the fundamental identities to simplify Use a graphing utility to check your result graphically sec x tan x sec x STEP 1 Multiply constants 7 sec x tan x sec x STEP 2 Factor LARPRECALCRMRP7 5 1 046 SBS sec x tan x sec x Need Help Read sec x tan x sec x 7 16 STEP 3 Apply the appropriate fundamental trigonometric identity and simplify sec x tan x 6 sec x 16 tan x 1

cot 8 Need Help Submit Answer 3 1 Points DETAILS sec x 1 cot x 01 Read It Match the trigonometric expression with its simplified form tan x csc x O tan x O sin x Need Help Submit Answer Watch it Read It LARPRECALCRMRP7 5 1 022

Use the values to evaluate if possible all six trigonometric functions If an answer is undefined enter UNDEFINED 26 26 cot p 5 sin p cos q tan p csc p sec 4

Determine whether the series n 1 6 5 10 OD Select the correct answer below and if necessary fill in the answer box within your choice OA The series diverges because it is the sum of two geometric series at least one with r21 OB The series converges because it is the sum of two geometric series each with r 1 The sum of the series is Simplify your answer OC The series diverges because lim n18 converges or diverges If it converges find its sum 6 57 10 The series converges because lim Simplify your answer 6 5 81x 10 0 or fails to exist 0 The sum of the series is

Write out the first few terms of the geometric series the inequality holds and the series converges What is the second term of the given series 8 What is a n 0 The general geometric series is a ar ar ar ar What is the first term of the given series n to find a and r and find the sum of the series Then express the inequality r 1 in terms of x and find the values of x for wh 5 What is r 0 If the series is convergent what is the series sum Substitute the expression in x for r in the inequality r 1 to obtain 1 Isolate x For what values of x does the series com 1 0 1