Application of derivatives Questions and Answers

Use the partial fractions method to express the function as a power series centere at x 0 and give the open interval of convergence f x n 0 f x The open interval of convergence is 13 x 3x 40

Suive ne equation The exact solution The solution round Iculster

b Show that if b varies then the polar equation r b csc 0 0 0 describes a family of lines parallel to the polar axis

a Identify the curve by transforming the given polar equation to rectangular equations r 3 cos 0

2 In each part a point is given in rectangular coordinates Find two pairs of polar coordinates for the point one pair satisfying r 0 and 0 0 27 and the second pair satisfying r 0and 27 0 0 2 3 2 a

Use the formula d 2rr cos 0 0 to find the distance between the two points indicated in polar coordinates 3 6 and 2 1 3

Find the rectangular equation if r 4 cos 0 4 sin 0 a c x y 4 x y 4 x y b d x y 4 x y x 2 y 2 4

8 Thangles ABC and A B C are s figures Determine the length o Side BCS 109103 B A 8cm 13cm C

or each table below select whether the table represents a unction that is increasing or decreasing and whether the function is concave up or concave down X 1 2 3 4 5 6 f x is Select an answer Select an answer x g x 1 92 2 125 3 152 4 173 5 188 6 197 f x 108 75 48 27 12 3 g x is Select an answer X h x 1 197 2 188 3 173 4 152 125 92 LO 5 6 h x is Select an answer Select an answer Select an answer

5 Find the volume of the solid enclosed by the planes z 0 y 0 z y 1 as well as the plane z y and the surface x y

This question has two parts Answer the first part correctly to get the second part Suppose you have a function f x whose average rate of change is always a constant number c That is suppose f x Part 1 of f x f a X a Rearrange this relationship to get f x alone on one side of the equals sign c for all inputs a and x

Use a calculator to evaluate the expression In In 62 25 62 25 22

Find the domain of the function g x In x 3 0 Type your answer in interval notation The domain of g is

Applications of Rational Functions Graph T x 98 6 x2 1 Vertical Asymptotes Horizontal Asymptote X intercepts Does our function cross the Horizontal Asymptote Y intercept 20 100 50 0 20 Give this equation context T x is the temperature degrees Fahrenheit of a person after x hours since they ate lunch with Susanna How does the domain change

10 8 6 4 2 6 5 4 3 2 1 2 O 8 10 1 12 3 The function graphed above is Concave up on the interval s Concave down on the interval s There is an inflection point at 4 5

The function f x 2x 39x 240x 1 has one local minimum and one local maximum Use a graph of the function to estimate these local extrema with output value This function has a local minimum at x value and a local maximum at x with output

5 4 3 2 3 2 2 3 2 3 4 The function graphed above is Increasing on the interval s Decreasing on the interval s

Complete the equation for the piecewise function graphed below 7 6 5 4 3 2 1 1 2 3 4 f x 2 1 2 6 5 4 3 2 1 8 1 2 3 4 5 6 if 6 x 2 if 2 x 1 if 1 x 6

Find the average rate of change of g x 4x 4 from X 3 to x 1

Assignme Previous Problem 1 point Consider the A Find the average

ent 10 Proble Problem List Next Proble the function f x e or mean slope of the function on the int alue Theorem we know there ex

Find the domain of the function f x O xl x 11 Ox x 11 and x 1 O xl x 11 O x x 10 O x x 11 and x 10 x 10 x 10x11

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Among the toolkit functions which of the following are true for the functions that are neither concave up nor down Check all that apply Can increase on some interval Can decrease on an interval Is made of pieces of lines Can have x with p 1

a Use transformations of the graph of y to graph the given function x 5 Part 1 3 Part 2 of 3 b Write the domain and range in interval notation 9 m The domain of the function is

Consider the following set of intervals Give its meaning in words Values that are Select an answer 2 Select an answer 1 Select an answer 3 Write it in set builder notation x Write it in interval notation values that are

Evaluate the limit using L Hopital s rule lim 3 cos 72 sec 9x Hi

nks Northern Virginia X Isl exe 10 u IgNslkr7j8P3jH IBhBKplvJLUg6NO6tj9qFltz6nQ 1 Applications RapidIdentity Homework C3S3 Question 10 of 10 1 point Question Atte 2 3 4

2 3 the expression without using 6 0 00 e

is equal to Alnr Bln s where A and where B Question Help Video Calculator

The expression log T 7y8 212 A log z Blog y C where A B Question Help Video

A large corporation with monopolistic control in the marketplace has its average daily costs in dollars given by C 1100 200x x The daily demand for x units of its product is given by p 90 000 100x dollars Find the quantity that gives maximum prof x units Find the maximum profit What selling price should the corporation set for its product x

Complete the table shown to the right for the half life of a certain radioactive substance GIS Half Life 10 1 days Decay Rate k

For functions f and g whose graphs are shown suppose that h x ln f x g x Find h 1 Y 3 2 f x E h 1 Note Enter an exact answer e g fraction and not a decimal approximation

Compute the Riemann sum for f x 21 2 on 1 4 using the partition 1 2 2 5 3 4 and the left endpoint of each subinterval the midpoint of each subinterval Now compute the Riemann sum for f x on 1 4 using a partition with six equal width subintervals and the right endpoint of each subinterval

22 In an arithmetic sequence a 42 and a 117 What is a 23 Matt s average score on the first 7 tests of his Pre Calculus course was 90 If he makes a 100 on the 3 test what will his new test average be 95

Solve the word problem below 24 What is the perimeter of a rectangle that has vertices 2 5 2 6 and 6 6 Estimate an irrational 78 answer to two decimal places

Solve the 24 What is the perimeter of a rectangle that has vertices 2 5 2 6 and 6 6 Estimate an irration 78 answer to two decimal places

The function f x ex is called the Select exponential function The number e is approximately equal to Round your answer to five decimal places

ve the following logarithmic equation Express irrational solution In x In x 12 4

graph f x 3x ANON X 4 2 by f x 3x 2 y 10 5 5 10 table of values 2 necessary 2 y 10 5 10 y 2

I III y YA a f x log x Select O IV FF 2 b f x log x Select O Select O f x log x X d f x log x Select O 2 X 2

ve the following exponential equation Express irrational solu 4 81 7 9 6 0

Questi Pa e following exponential equation Express irrational solutions in ex P 49

Use the true conditional statement shown below State If a number is negative then its cube is negative C If the cube of a number is not negative then th

2 Let f x y xy and let D be the solid unit disk D x y x y 1 Find the location and value of the absolute max and the absolute min of f on D Use the method of Lagrange multipliers on the boundary

Simplify the Boolean expression ABC A B B C A B C

Let statements p q r and s be as follows p ZA and ZB are a linear pair q ZA and ZB are supplementary angles r ZA and ZB are adjacent angles s ZA and ZB are adjacent and supplementary angles Substitute for p q r or s and write the statement the way you pos Choose the correct answer below OA If ZA and ZB are adjacent and supplementary angle OB ZA and ZB are a linear pair if and only if ZA and 4 n

31 a 3log 5 32 a en V3 b 5logs 27 b eln 1 m c en 10 c 10log 13

Algebraically find the inverse function of f x 3 5e x Graph f f and the line y x on the same screen and check whether the graphs of f and f are reflections about the