Differentiation Questions and Answers

Angies Identify the figure as a line half line ray line segment D A

0 2 pts 397 Det The altitude of a triangle is increasing at a rate of 2 centimeters minute while the area of the triang is increasing at a rate of 5 square centimeters minute At what rate is the base of the triangle changing when the altitude is 8 centimeters and the area is 91 square centimeters cm min Question Help Vidon

The area of a circular healing wound is given by A r The radius is decreasing at the rate of 3 millimeters per day at the moment when r 47 How fast is the area decreasing at that moment Select an answer

30 1 Find the arc length of the polar curve r e 8 from 0 0 to 0 2 FUSE OVras OCATERER SAN CATER BETEOROlar FELANGE a c AZIE O PO SUPERTARIAS Portman Bla SUP BESATUAN 10 e 1 3 LAND ROpac 10 e 1 3 DAVALCREST PERFE AND THE Poid Anal SADEST Nemme MERTE Mrizare TEREN WTHREE b d 10 e 1 3 10 e 1

A business wants to set up a three sided fence to enclose a rectangular area of 2 000 square feet in the front of their store If materials for the front of the fence that face the street cost them 20 per foot and the cost for the two other sides cost 15 dollars per foot find the minimum cost for the project too the nearest cent Solve the problem in 2 different ways First use the method of LaGrange Multipliers and then use the methods you learned from calculus 1 when working with a function of one variable By doing this both ways you will connect your knowledge and get the most out of this word problem Do not include units which are in dollars

100x The dose response for a specific drug is f x x 0 11 from a dose of a grams of a drug where 0 x 1 5 Find f 0 5 and select the appropriate units f 0 5 percent relief per gram where f x is the percent of relief obtained

Let f x X Enter an antiderivative of f x 3 2 3 6e X 6e

f x wwwwwww SLO 7x 8x 3 VX 8x F z 212 18 3 2 2x then

If f x f x f 1 7x 5 2x 3 11 2x 3 find

Find the function R that satisfies the following conditions R T R x 6 0 3x R 0 7

If f t t 4t 4 6t 3 24 721 54 12 Find f 5 find f t

Find dz dx z 3 2 3 if z 8x 8x y 8y

Find fy x y if f x y 8x 8y 9 fy x y

Find the indicated derivative dz if z In x e6

Find the indicated derivative A 9 if z In x

A rectangle has an area of 384 square inches Its width is eight inches less than twice the length Find the measures of the length and width of the rectangle The length measures The width measures inches inchoo

Consider the function f x x 50x 11 4 x 11 This function has an absolute minimum value equal to which occurs at x and an absolute maximum value equal to which occurs at x

25 The figure below consists of 4 squares of D

18 Solve the following logarithmic equation In x 31 ln 4 3x 5 ln 2 x 2 O r 1 x 0 5 x 0 25 None of the above

9 Factor the following expression completely 3x 3x 4 x 8 3x 4 3 8r 3x 4 6x 12 24x 3x 4 11 12 3r 3r 4 11x 4 Or 3r 4 11z 4 3r 3r 4 5x 12

7 If f x 3x 9 find and simplify 3a 6h 3h 12a 6a 3h 3h 3a 9h 6a f a h f a h where h 0 2

4 Given log 3 3 4 2 4 log3 9 1 12 1 4 9 what is log 9

2 A closed box has a square base with side length I feet and height h feet Given that the volume of the box is 29 cubic feet express the surface area of the box in terms of 7 only S 1 21 1161 116 S 1 21 1 S I 21 1161 S I 61 None of the above

3 Rationalize the denominator and simplify completely x 4 x 2 x 4 x 2 O x 4 x 2 x 4 x 2 None of the above x 16 x 2

QUESTION 16 Find a unit vector in the direc v 20i 21j 29 29 Uv 20 21 j 12 Uy 29 35 29j

Find the global maximum and global minimum values of the function g 0 50 7 sin 0 on the interval 0 Round your responses to the nearest thousandth The global minimum value The global maximum value

Find s t where s t represents the position function and v t represents the velocity function v t 6t s 0 8 11

A fence is to be built to enclose a rectangular area of 250 square feet The fence along three sides is to be made of material that costs 3 dollars per foot and the material for the fourth side costs 12 dollars per foot Find the length L and width W with W L of the enclosure that is most economical to construct L W

A rectangular storage container with an open top is to have a volume of 26 cubic meters The length of its base is twice the width Material for the base costs 13 dollars per square meter Material for the sides costs 8 dollars per square meter Find the cost of materials for the cheapest such container Total cost Round to the nearest penny and include monetary units For example if your answer is 1 095 enter 1 10 including the dollar sign and second decimal place

Find the length L and width W with WL of the rectangle with perimeter 48 that has maximum area and then find the maximum area L W Maximum area

Use the graph to the right to write an e

Measures Solve the system of linear equations by graphing X 6 y 5

What is the derivative of y after we simplify the answer In 10 1 f x 2 x 1 f x In 10 1 f x In 10 1 f x 1 x 2 x 1 x In 10 1 f x y log 1 f

Which of the following is the augmented matrix of the system of equations x 2y z 1 2xy 3z 4 3x y2 2 Select one a b OC O O d d 1 2 2 1 34 2 2 1 23 13 T 1 1 1 HJ Clear my choice 0 0

A baseball diamond is a squa a How many meters does a b b How many kilometers c How many millimeters a The batter ran meters Type an integer or decimal ro

1 point A 2 4 6 B 3 4 Check ALL of the following Cartesian products to which the following elements belong d 4 4 OA Ax B B Bx A C AXA D Bx B c 2 2 DA AXA B AxB C B x B D Bx A a 2 3

1 point How many different ways can a race with 5 runners be completed Assume there is no tie Your answer is

7 1 Basic Terms and Conversions Within the M System A mountain that gets many visitors opy meters higher is the

Evaluate the definite integral 1 0 1 7x 6x 5 dx 7x 6x 5 dx Simplify your answer

4 Express the equation in exponential form A log27 3 3 B logs 0 008 3

Find the indicated value of the function f x y 2x 9y 5 f 4 2 Select the correct choice below and if necessary fill in the answer box to complete your choice OA f 4 2 Simplify your answer OB f 4 2 is undefined

One pump removes 6 dal of water in 1 min water faster Explain

Integrate as indicated Assume g x 0 whenever In g x is involved 8x 1 dx 4x 5 8x 4x 5 dx ww

Find the derivative of f x and the indefinite integral of g x f x 7x g x x6 f x

Flestan coordinates of a point are given a 6 6 b i Find polar coordinates r 0 of the point where r 0 and 0 0 2 r 0 ii Find polar coordinates r 0 of the point where r 0 and 0 0 2 r 0 4 4 3 i Find polar coordinates r 0 of the point where r 0 and 0 0 2 r 0 ii Find polar coordinates r 0 of the point where r 0 and 0 0 2 r 0

The equation y log x 3 has a vertical asymptote at X

Consider the function f x x a Compute the derivatives f 4 f 4 and f 4 You do not need to simplify your answer completely b Find the Taylor polynomial Po x P x P x and P3 x for f x centered at x 4 c Create a graph showing both f x and P x Then create a second separate graph showing both f x and P3 x Write a sentence or two describing the ways that P x is and is not a good approximation of f x and discuss the ways P3 x is or is not a better approximation of f x d Approximate f 7 using the 3th order Taylor polynomial of f x centered at 4

For each of the statements below state whether the statement is True and False otherwise Clear justify your answers a Let F x be an antiderivative of f x such that F 1 0 Then the area under the graph of F x between x 1 and x 9 is f 9 b You are investigating your favorite youtuber You learned from your investigations that she launched her YouTube channel with 30 subscribers on April 1 2020 Also each week the number of new subscribers increased by 25 from the previous week Then the number of subscribers n weeks after April 1 2020 is represented by the finite geometric series 30 30 1 25 30 1 25 30 1 25 converges then the sequence converges to a number different from c If the series zero k 1

2 Find polar coordinates of all points at which the polar curve has a morizontal or a vertical tangent line r a sin 0 27

Using the properties of exponents and logarithms find the value of x in 19 2lnx 25