Application of derivatives Questions and Answers

10 Answer 5 Step 1 of 2 Use the graph to determine the locations and type of the local extrema Write DNE for all extrema that do not exist Separate multiple answers with a comma if necessary Local minimum at Local maximum at Yx Keypac Keyboard Shortca

Apply the power property of logarithms Assume that all variable expressions represent positive real numbers log 8t 1 3 log 8t 1 log

Apply the power property of logarithms Assume that the variable expressions represent positive real numbers In 2 In 2 DinO

What is the average rate of change of f x from x 10 to x 8 Please write your answer as an integer or simplified fraction f x 6x 3

The top and bottom margins of a poster are each 9 cm and the side margins are each 6 cm If the area of printed material on the poster is fixed at 864 cm2 find the dimensions in cm of the poster with the smallest area width height WW x cm cm X 2 calcP Operati Functio Symbol Relatio Sets

A motion is defined by the following parametric equations x sin t y 2cos t 1 a Show that the particle passes through the point 2 2 F b Find the slope of the tangent line to the curve the orbit at this point c By using T t T d y dx Find the time t at which the particle passes through this po determine whether the orbit is concave up or concave down near this point d At what speed does the particle go through this point e Sketch the orbit and indicate the direction of the motion

stion 1 of 15 Step 1 of 1 Answer V 10 10 Correct Selecting an option will display any text boxes needed to complete your answer Increasing on one interval Decreasing on one interval Constant on one interval O Increasing on one interval and Decreasing on another Increasing on Decreasing on 10 X

Find all the values of x for which the following geometric power series converges b Find the rational expression to which this series converges x 3 32n n 1

Given the complex number z 3 cos i sin and 8T 8T 22 3 cos i sin express the result of 2 22 in rectangular form with fully 9 21 9 simplified fractions and radicals

Solve the word problem below 85 24 An ice cream cone that was accidently dropped from the top of a building can be represented by the function y t 41 21 where t is time in seconds and y is measured in meters Based on this function what is the velocity of the ice cream cone after it has fallen for 3 seconds

21 11 2 35 then 2x 7 Estimate your answer to 1 decimal place 169 31 22 13 13 7 of the sequence 23 831 31 and are the first three terms of an arithmetic sequence what is the sum of the first 21 terms 1375 5 Mark s morning class scored an average of 89 25 points across 4 tests His evening class scored an average of 94 50 points across 4 tests What was the average test score between both classes across all 8 tests Estimate your answer to 2 decimal places 45 94

Mark s morning class scored an average of 89 25 points across 4 tests His evening class scored an average of 94 50 points across 4 tests What was the average test score between both classes across all 8 tests Estimate your answer to 2 decimal places BU

An ice cream cone that was accidently dropped from the top of a building can be represented by the function 31 4 2r where is time in seconds and jt is measured in meters Based on this function what is the velocity of the ice cream cone after it has fallen for 3 seconds 42

Evaluate the integral xyz dS where S is that part of the plane z 8 y that lies in the cylinder x y 16 using S the method of your choice As a first step set up the surface integral for the given function over the given surface S as a double integral over a region R in the xy plane SS O xyz dS S R Type an exact answer using radicals as needed dA

Find the divergence of the following vector field F 8x 5y 8z The divergence of F is

Find the divergence of the following vector field F 4x 4y 9y 92 52 5x The divergence of F is

Suppose that 2 J of work is needed to stretch a spring from its natural length of 36 cm to a length of 50 cm a How much work is needed to stretch the spring from 38 cm to 46 cm Round your answer to two decimal pla 0 94 X J

Use this picture for questions 4 6 Find the limit or put DNE if it doesn t exist lim f x Find the limit or put DNE if it doesn t exist lim f x 11 x 2 11 R

Use the four rectangles shown to approximate the area of the region below the graph of f x 18x x over the interval 8 16 The area is Round your answer to the nearest whole number as needed 90 80 70 60 50 40 30 20 10 0

Estimate the area of the region above the x axis and under the graph of the function from x 0 to x 4 14 12 10 2 04 N 6 The area of the region is approximately Round your answer to the nearest whole number

10 5 population in 2010 2015 and 2020 2 World Population The following table shows U S Census Bureau estimates for key world population benchmarks A geometric sequence is the discrete analog to an exponent function Both a geometric sequence and exponent function assume a constant multiplicative rate of change Let w be a geometric sequence that represents the world population in billions of persons n years after 1959 Use w 3 00 as the initial condition for the sequence Population in billions Year 1959 1974 1987 1999 2012 345 6 a Assuming an annual percentage increase of 1 62 in world population write a recursive formula for the sequence w b Write an explicit formula for the geometric sequence w in part a Use exponential regression to confirm the accuracy of this model c Use the formulas from parts a and b to estimate the world population in 2010 2015 and 2020 d The actual annual growth rate in world population has slowed from 2 22 in 1963 to 1 09 in 2013 so a logistic growth model may be more appropriate than an exponential model Use the data in the table and logistic regrosci to optimate the world

What is 2sin a cos a cos 2 a sin 2 a equal to

Show that the equation that information sin x X x 0 has a solution Provide all the necessary justifications for your solution If you use

The total number of inches of rain during a storm in a certain geographic area can be modeled by 2t Use the graph to approximate the number of inches of rain during a storm that lasts 8 hour t 8 2 1 8 1 6 1 4 1 2 1 0 8 0 6 0 4 0 2 1 2 3 4 5 6 7 8 9 10 1 inch 5 inches 2 inches 0 4 inches

a Graph the function y 3e Be sure to identify any asymptotes or intercepts Graph the function y log x 3 Be sure to identify any asymptotes or intercepts

Let f and g be the functions described by the following graphs Graph of f YA x a Fill in the blanks using interval notation The domain of fis The domain of g is gof 2 b Is g a one to one function Answer yes or no c Evaluate the following if they exist g 0 f g 2 gog 2 The range of fis The range of g is Graph of g Y 2

Write a rational function that has the vertical asymptote x 1 and the horizontal asymptote y 2 For the toolbar press ALT F10 PC or ALT FN F10 Mac

3 The functions f and g are defined as f x and g x x 7 X f a Find the domain of f g f g f g fg ff and 7 b Find f g x f g x fg x ff x g x and x

Given the matrices A and B shown below find A B 3 5 3 B Rows 2 Columns 2 18 12 24 16 4 4

1 point Problem 8 A culture of yeast grows at a rate proportional to its size If the initial population is 8000 cells and it doubles after 4 hours answer the following questions 1 Write an expression for the number of yeast cells after t hours Answer P t 2 Find the number of yeast cells after 5 hours Answer 3 Find the rate at which the population of yeast cells is increasing at 5 hours Answer in cells per hour

Find the component form of the indicated vector Let u 3 1 V 6 6 Find 9u 2v 27 14 15 21 18 24 392

Given the matrices A and B shown below find B A A Rows 20 1 6 2 0 5 B Columns 204 24 3 6 18 12 9

Evaluate the indefinite integral 1 7a 11 4 da 2 a 1 2 9 3 sin 0 cos de 99 V 7x 11 ac dx du dy 54 55 1 x 1 da U sub with solve for x dx du du dx visinx d c cos xdy sin 0 cos de idu cos xdx X 1 v U 1 X U CSCX 4 csc 0 cot 0 d csc0 cot o do cscx Cotxd du co4 idu csc x cox x xx Sxcus xx 5 50 no su 8 U x Su 00 C 3

Find the component form of the vector v 4 70 1 71 O 4 70 1 82 O 0 94 0 34 O 1 71 4 70 Y 5 20

Find the component form of the vector v 11 O 7 07 8 43 O 0 77 0 64 O 7 78 7 78 O 8 43 7 07 Y 140

6 Find the area of one loop of 1 cos 80 1 5 1 5 1 0 0 5 0 5 A 1 0 1 5 05 1 5

Find the component form of the vector v 220 41 O 26 35 31 41 O 31 41 26 35 O 0 77 0 64 O 0 64 0 77

Calculate the left Riemann sum for the given function over the given interval using the given value of n When rounding round your answer to four decimal places If using the tabular method values of the function in the table should be accurate to at least five decimal places HINT See Example 2 f x 124x 31 over 0 2 n 4

Given the matrices A and B shown below find A B A 0 2 0 5 3 1 3 2 Rows 2 Columns 2 B 28 4 20 0 8 8 40 48

Determine if the following function has an inverse function r x x 4x

Given the matrices A and B shown below find A 2B A Rows 2 3 1 3 0 4 2 3 B Columns 20 10 1 8 9 10 2 6 9

20 45 What is the range of f x 5 11x 4 1 0 y 2n 4 y 6 A D B E 5sys5 6 y 4 C All real numbers

Calculate each of the following limits x 7 lim x 3x 2 17 85

Consider the following function a 0 n 3 0 x 0 1 a Approximate f by a Taylor polynomial with degree n at the number a T3 x b Use Taylor s Inequality to estimate the accuracy of the approximation f x n x when x lles in the given interval Round your answer to five decimal places R3 x c Check your result in part b by graphing IR x y 0 0001 0 0002 0 0003 0 0004 0 0005 0 0006 0 00071 0 0001 0 0002 0 0009 0 0004 0 0005 0 0005 0 0007 0 02 0 04 0 06 0 08 0 10 X 0 02 0 04 0 06 0 08 0 10 0 0007 0 0006 0 0005 0 0004 0 0003 0 0002 0 0001 0 02 0 04 0 06 0 08 x 0 10 0 0007 0 0006 0 0005 0 0004 0 0003 0 0002 0 0001 0 02

5 Find for the curve t sin t t y t t t What is the minimum y value W does it occur

Find the Taylor polynomial T3 x for the function f centered at the number a f x e sin 3x a 0 T3 x Graph fand T3 on the same screen 201 0 4 0 2 15 1 0 0 5 0 5 1 0 151 0 4 02 20 115 1 0 0 5 10 0 2 D 4 CL6 0 8 1 0 0 2 0 4 OLG 0 6 1 0 x 201 15 1 0 0 5 27 x 0 4 0 2 0 2 0 4 0 6 0 8 1 0 0 4 0 2 0 5 1 0 20 13 1 3 1 0 0 5 65 1 0 1 51 0 2 0 4 0 6 0 8 2

Evaluate the integral Assume that B is a real number and that B 4x12x x dx

Determine the area that is bounded by the following curve and the x axis on the interval below Round your answer to three decimal places y x 4 6 x 0

Evaluate the definite integral 1 1 2 x 1 2 S X dx t 1 t dt x 1 23 12 1 1n 11 1 69 SLE dy 5 3 dx 3 m

Use the Fundamental Theorem of Caclulus Part 1 to find the derivative 1 de f 1 dt dx t 1