Differentiation Questions and Answers

Find the future value at 8 interest compounded continuously for five years for the continuous income stream with rate of flow f t 560 Round answer to the nearest dollar 835 2308 2750 3443

Determine which of A B and C are equal before evaluating two decimal places 2 A 007 2 1 dt B 1 0 14 0071 dt C 2014 COLOR Choose the correct answer below A The expressions B and C are equal B The expressions A and B are equal c The expressions A and C are equal OD The expressions A B and C are all equal 0

Determine which of A B and C are equal before evaluating the expressions Then evaluate each expression to two decimal places 2 2 A S007 2 1 dt B 0 14 0 071 at C 2014 fe 0 071 at dt dt 2 Choose the correct answer below O A The expressions B and C are equal B The expressions A and B are equal OC The expressions A and C are equal OD The expressions A B and C are all equal E None of the expressions are equal

5 Convert the rectangular equation to polar form x 3 y 9

1 point Let U Universal set 0 1 2 3 4 5 6 7 8 9 A 2 3 4 5 8 9 and B 0 2 5 9 List the elements of the following sets If there is more than one element write them separated by commas A AUB AUB ANB

e given function f to answer parts a through f below 2 Inx G OB Question 19 6 4 75 Part 6 of 8 Ay OC m the graph determine the range and any asymptotes of f nge of f is 0 00 your answer in interval notation ine the vertical asymptote of f Select the correct choice below and if nebessary fill in the answer b mptoto off is Y 0 Simplify your answer

e the given function f to answer parts a through f below f x 4 log5 x 2 e your answer interval notation Choose the correct graph of f below B Ay Question 20 6 4 83 Part 5 of 8 om the graph determine the range and any asymptotes of f G

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2 20 You may enter the exact va Calculator

d y dx 5 Find at t 2 for x t 1 y t t a c 213 113 b d 580 318

d y dx 5 Find at t 2 for x t 1 y t t 2 a c WI3 WIN b d 5 8 mi co 8

8 Find the slope of the tangent line to the parametric curve x 4 cos t y 3 sin t when t 2 a c 4 1 b d 0 3 4

2 Find the interval of convergence for 1 a 1 1 b 2 2 c 0 5 0 5 d 0 00

Answer true or false The interval of convergence for a True b False x 4 3 is 7 1

a b Express the given equations in polar equations x y 7 4 xy 3

1 Find the rectangular coordinates of the points that the polar coordinates are given a 7 2 3

Write the equation of the circle centered at 4 0 with radius 4 Enter an algebraic equation more

3 Find the average rate of change of g x 8x x4 interval 2 1 on the

The monthly profit from producing and selling x units of a product is given by the formula below P x 0 3x 660x 120 000 Producing and selling how many units will result in a profit for this product Use an interval to describe how many units can be produced and sold to produce a profit Type your answer in interval notation

16 The probability that Stacy will pass a math test is and the probability that Sophie will pass the same 82 6 What is the probability that Stacy will not pass her test and Sophie will math test is

above is NOT correct limit Use l Hospital s R

What is the domain of the function in the graph 20 P 18 160 14 12 10 8 6 4 2 4 00 d 6 O 10 p 16 00 p 6 O 10 d 16 d

Find the domain and range of the function graphed below 5 4 3 2 1 Domain 5 3 2 1 1 2 3 5 2 3

Find the domain of the function graphed below 8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 F 1 2 3 4 Domain 6 7 8 1 2 3 4 5 6 7 8

5 2 1 6 5 4 3 2 1 1 2 3 5 3 4 5 Write the domain of the function using interval notation

Answer the following question 22 In an arithmetic sequence a 77 42 and a 117 What is asa Chic Pre Calculus course was 90 If he makes a 100 on the 8th

1 2 Domain and Range What is the domain of the following function x 7 f x X 3 Ox 3 O 7 3 U 3 0 3 0 O 7 All real numbers

1 2 Domain and Range Find the domain of the function graphed below 5 4 3 2 1 Domain 6 5 4 3 2 2 3 4 5 6 2 3 4

Draw the graph of f x 6 Plot two points have integer values for both x and y 10 9 8 7 6 5 4 3 2 10 9 8 7 6 5 4 3 2 1 IN 1 2 3 4 567 5 6 7 8 9 10 1 2 3 4 6 7 8 9 10

Solve for T log z 4 log z You may enter the e

Evaluate the limit using L Hospital s rule if necessary For 1

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1 2 Write the equation in expon log13 1 0

2 40 30 20 Slope of tangent line at 1 8 4 1 18 2 8 10 12 14 The graph above is that of f x in blue The slope of the tangent line at a point on the graph of f x is also given The point on the graph can be moved as needed Suppose that g x 4x a If h x f g x determine the value of h 1 h 1 b If m x f x g x determine the value of m 1

4 3 2 3 2 1 B 23 2 Use the graph of the function f x shown above in blue and its tangent line at x 0 in red determine the value of the following derivatives If h x f x then h 0 If H x f x x then H 0

4 324 2 2 1 1 2 3 7 2 3 4 Suppose that f x ln x 1 1 The graph of the function g x is shown above in bl together with its tangent line at x 0 in red If h x f x g x determine the value of h 0 h 0

Find the slope of the tangent line to the curve 4x 3xy 4y 171 at the point 3 3

Find the following derivatives using the table X 1 2 f x 1 4 f x 1 2 g x g x 1 4 2 4 3 110 2332 c Find h 2 if h x 4 3 4 1 a Find h 2 if h x 5f x 2g x h 2 b Find h 2 if h x f x g x h 2 3 f x g x

d Find cos x xe You need not simplify your answe dx

Graph T x 1 98 6 Vertical Asymptotes Horizontal Asymptote X intercepts

Use logarithms to solve the exponential equation You may leave your answer in exact form or round to 4 decimal places In either case show all the steps in your work 5 2 3 4 x

Combine the following expression into a single logarithm 2 log a log y log 7z Be sure to show all the steps in your work

The exponential function f x 9 has th Select asymptote y slant horizontal vertical This means that as x we have 9

Determine the absolute extrema s if any of f x 2 3x 2 2 x 2 on the interval 0 7

59 66 Change of Base Formula Use the Change of Base Formula and a calculator to evaluate the logarithm rounded to six decimal places Use either natural or common logarithms 59 log 5 61 log3 16 63 log 2 61 65 log4 125 67 Change of Base Formula Use the Change of Base Formu to show that 60 logs 2 62 log692 64 log 532 66 log12 2 5 log3 x In x In 3 Then use this fact to draw the graph of the function f x log3 x

Consider the function f x x 12 A Find f 12 B Use Theorem 7 page 156 of the Stewart Essential Calculus textbook to find f 12 12 C Calculate f x and state domain and range of f Use interval notation If needed enter inf for or inf for 0 f x Domain Range Calculate f 12 from the formula for f x and check that it agrees with the result of par

If f x sin 6x 2 then f x 0 Note The inverse of sin x can be entered as arcsin r or asin

Find the first derivative of f x f x tan

Find the first derivative of f x 5 sin

Find the first derivative of f x f x x tan