Differentiation Questions and Answers

tan 13x 12 OA 2 3 2 3 4 OB 2 3 4 On 2 3 O C

cos x 2 sin x cos x secx O A cot x OB cScx OC sec x OD csc 2x

Determine the domain of the function f x 49 36x OA OB O C 77 6 6 0 6 17 00 OD

17 sin 0 35 300

Find the missing side lengths Leave 43 45 60 3 3 2 X X 7 3 60 swens 100 bano

37 cos 1 2

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

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

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

Take the log In of both sides Simplify using Log Laws Take the derivative implicitly dy Solve for y dx ples Cor 1x 1 2

h x ln xe 2x

fopl fit x 2 42 of t 2 X

An amusement company maintains records for each video game it installs in an arcade Suppose that C t and R t represent the total accumulated costs and revenues in thousands of dollars respectively t years after a particular game has been installed and the derivatives C t and R t are the following functions C t 5 and R t 8e 0 1t Find the area between the graphs of C and R over the interval on the t axis from 0 to the useful life of the game and interpret the results What is the useful life of the game years Round to the nearest tenth as needed SILB

A company determined that the marginal cost C x of producing the xth unit of a product is given by C x x 4x Find the total cost function C assuming that C x is in dollars and that fixed costs are 6000 C x CO

f x x 8x 24x g x 19x 52 The area is Type an integer or a simplified fraction

F cos2x cosx 0 denkleminin 0 2n aral ndaki k klerinin lam ka radyand r

Integrate x x 2dx

Evaluate 2 2 x x 1 5 dx 1 5 x x 1 dx 1

Evaluate Be sure to check by differentiating Sex 20 dx S 6x 2 dx Type an exact answer Use parentheses to clearly denote the argument of each function

Evaluate Assume u 0 when In u appears Sx ex dx x x x dx CT et epower

The tables to the right give price demand and price supply data for the sale of soybeans at a grain market where x is the number of bushels of soybeans in thousands of bushels and p is the price per bushel in dollars Use quadratic regression to model the price demand data and linear regression to model the price supply data Complete parts A and B below A Find the equilibrium quantity and equilibrium price The equilibrium quantity is thousand bushels Round to three decimal places as needed Price Demand p D x 6 64 6 54 6 45 6 38 6 35 X 0 10 20 30 40 Price Supply P S x 6 34 6 40 6 45 6 48 6 53 X 0 10 20 30 40

2 6x 3 Find the constant term in the expansion of 6x

In 2012 34 1 of all glass containers were recycled A beverage company used 350 000 lb of glass containers per year After recycling the amount of glass in pounds still in use after t years is given by N t 350 000 0 373 a Find N 7 and explain its meaning b Find N 7 and explain its meaning c When will 6 of the original amount of glass still be in use a N 7 351 58 lb Round to two decimal places as needed The expression N 7 means that after year s the amount of glass still in use N 7 pounds N 7 pounds per year N 7 pounds per year N 7 pounds

An office machine is purchased for 7300 Assume that its salvage value V in dollars depreciates according to a method called double declining balance by 30 each year and is given by V t 7300 0 70 where t is the time in years after purchase a Find V 3 and explain its meaning b Find V 3 and explain its meaning c When will the salvage value of the office machine be half of the purchase price a V 3 2503 9 Round to the nearest cent as needed The expression V 3 means that after 3 year s the salvage value b V 3 Round to the nearest cent as needed is V 3 dollars

A scientist has two cultures of bacteria Culture A starts with a volume of 3 ml and doubles every 4 hours Culture B starts with a volume of 2 ml and doubles every 3 hours What should be the starting volume of culture A if we want the two cultures to have the same volume after 12 hours O a 2 O b 3 O c 4 O d 5 O e 6

In some chemical reactions the rate at which the amount of a substance changes with time is proportional to the amount present For example this is the case as 8 glucono lactone changes into gluconic acid a Which of the following differential equations is satisfied by y the quantity of 8 glucono lactone present at time for some constant k dy dt O dy dt dy dt O dy dt k y ky 11 ky eTextbook and Media 4 hours

The equation A t 8000e0 055t gives the balance after t years of an initial investment of 8000 dollars which pays 5 50 compounded continuously dA a Find a formula for dt b Find and interpret A 10 Include appropriate units c Compare the approximation of 763 to the actual change Report your answer to two decimal places a dA dt 440e0 055t b A 10 Round up to the r dollars increased in the total amount per yearly increase in the investment time period years per dollar increase in the initial investment dollars years increased in the total amount per dollar increase in the initial investment

A company s total cost in millions of dollars is given by C t 100 40et where t is the time in years since the start up date The graph of C t is shown to the right Find each of the following a The marginal cost C t b C 0 c C 5 d Find lim C t and lim C t t 0 t a C t 40et Do not include the symbol in your answer b C 0 40 million per year Simplify your answer Do not include the symbol in your answer Ay 150 75 15 30 c C 5 per year Simplify your answer Round to the nearest thousand as needed Do not include the symbol in your answer 57

2 Evaluate fx cos x dx as an infinite series

Find the Taylor series for f x sin x centered at a EIN

Find the derivative of the function g x g x e 3x 1 4 3x Pe 4 3x

Find the derivative of 9e Use e x for e 91 21 cos 2x Hint use product rule and chain rule Now find the equation of the tangent line to the curve at x 0 Write your answer in ma b format

Use Green s Theorem to evaluate the line integral along the given positively oriented curve Scxydx x y dy C is counterclockwise around the triangle with vertices 0 0 1 0 and 1 4

en y t 3t 6t 7 and y 0 12 find y t

1 5 points Which of the following is a critical point of the function f x ln x 8x A x 1 16 B x 16 fx ln x 8x C x 1 4 D z 4 E f x has no critical points

Calculate the derivative of a function A r r when r 8

2 3 A No solution 7 6 5 4 3 2 10 B x 0 6 or x 2 1197 32 10 C All real numbers D x 46 4 or x 0 4 0 Find each quotient 2 VIAGIN A C 10 7 7 10 B D 34 35 10 7 A 15b 2b 20 C 15b 2b 8 5 789 3456 05 10 15 20 25 30 35 40 45 50 Simplify each difference 3 36 3b 1 86 7b 3 5b b 6b 3b 4 5b B 15b 2b 14 D 15b 2b 20 8h

Calculate the following expressions A Given h x x 2 x 4 h x

Twas The Night Bef 4 f x x 8x 11x 20 Zero x 4 Three of Santa s reindeer s names begin with the letter D What are those names SEAXE AD 10 MB 11 MA

1 f x 6x 2 x

1 Use the definition of the derivative to show y f x x is f x 2x 2 Find the derivative f x if f x x sin x 3 Find the derivative f x if f x ln x x 1

4 Find the derivative f x if f x 11 m

3 Given the graph of the function f a below answer the following questions 50 40 30 20 10 2 3 Hin y f x 5 a Is f x one to one Explain b Use the graph to approximate f 20 c Use the graph to approximate f 20 x

Consider the function y f x graphed below Give the

Find the exact value of COS O 15 15 4 os sin 2 15 15 O 4 15

Solve for 2 372 1 81 Olog 82 7 28 7 5

Identity the expression that completes the following equation so that it is sin z 1 cos z a 1 sin z CoS z Ob 1 cos x Od 1 sin r c cos z d sin a

The price of a home is 270 000 The bank requires a 5 down payment at the time of closing The mortgage on the house is a 30 year fixed rate mortgage at 7 Use this information to find the amount of the monthly payment Round your answer to the nearest cent Use the formula below to solve the problem Payment 2 nxt 1 1 1 1 695 2 1 796 3 1 807 PL n 4 1 707

6 Which substitution will you make to evaluate the indefinite integ x 1 dx x 4x a x 1 b x 4x c x 1 x 4x

4 3 x2 Find the derivative