Application of derivatives Questions and Answers

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

Find the sum of the series 1 In 7 In 7 In 7 21 31

A person 6 feet tall is walking away from a lamp post at the rate of 55 feet per minute When the person is 4 feet from the lamp post his shadow see dashed line is 10 feet long Find the rate at which the length of the shadow is increasing when he is 20 feet from the lamp post The length of the shadow is increasing at a rate of 6 ft feet per minute

Find the work done on a particle moving from J to K if the magnitude and the direction of the force is given by F J 8 6 K 3 3 F 1 6j

A function f satisfies the following conditions lim f x 6 x limf x 2 x 0 limf x x 6 What can be said about this function O This function has both a horizontal and a vertical asymptote O This function may have a horizontal or vertical asymptote but with the given information we cannot fi O This function has a vertical asymptote but we can t tell whether there is any horizontal asymptote or

You spin this spinner 3 times Find the probability of these 3 events P red odd 3

Find all points if any of horizontal and vertical tangency to the curve z 5 3 cos 0 y 4 sin 0

A pilot flies in a straight path for 2 h 30 min She then makes a course correction heading 7 to the right of her original course and flies 3 h in the new direction If she maintains a constant speed of 695 mi h how far is she from her starting position Please round the answer to the nearest integer

A ball of radius 10 with a cylindrical hole of radius 9 drilled through its center has volume volume

s the eighth term of the recursively defined sequence 3 and an 3 1 3 1 8 for n22 hth term is

Find the 4th term in the sequence defined recursively by 9 3 an 2a 1 5 Select one O a 4 O b 11 c 7 O d 1

9 Find the area between the curves y sketch of the curves and shade the area to be found sin z y cos over the interval 7 7 Include a detailed

The boundaries of the shaded region are the y axis the line y 1 and the curve y Find the area of this region by writing a as a function of y and integrating with respect to y YA 1 y 1 y 4 x

Let f x Find T 31 10 I 71 8 1 Domain in interval notation 1 U 1 8 U 8 00 2 Y intercept s at the point s 0 5 3 X intercept s at the point s 2 61288786 0 4 X value of any holes DNE 5 Vertical asymptotes at x 1 8 6 Horizontal asymptote at y 1 7 Oblique asymptote at y x 7 Question Help Message instructor E Calculator OF X q OF syntax incomplete 4

8 10 Pts Let F 3x z 2y 3x 3y z 5xe y a Find curl F VxF b Use Stoke s theorem to evaluate f xF ds where S is that part of the sphe

x 2 2 4 21 If f x 1 4 22 8 22 16 if a 4 if x 4 find lim f x if it exists Is lim f x 4 2 4 if a 4

cos a axo 1 2 18 Find lim and justify your solution

15 lim BITK 16 evaluate the given limit 1 9x 5x 4x64x2x3

In problem 14 graph of a function f is shown Refer to the given graph to find the limits 14 lim f x 2118 lim f x lim f x lim f x f m

1 lim 2 3 to 3 hnd the limit by app 2r 10 z 1

The velocity of a car is f t 8t meters per second Use a graph of f t to find the exact distance travelled by the car in meters from t 0 to t 8 seconds Distance

What relevant conclusion can be drawn from the following promesise If I play hockey then I am sore the next day I use the whirlpool if I am sore I did not use the whirlpoo OI played hockey O I m sore OI use the whirlpool OI didn t play hockey

Using what you learned in Lecture 1 only explain in English how you will find the derivative of f x Then perform the operations that you explained type the mathematical expressions and find f x 6x5 3 2x 3

A boat is traveling at 34 knots in a direction of 68 It encounters wind moving at 11 knots in a direction of 15 What is the true velocity and direction of the boat Round to the nearest whole number O 23 knots 34 O 41 knots 55 41 knots 34

Some sanitation workers sifted through some recycling and trash to see whether people had correctly sorted their plastic bottles Plastic 2 Plastic 4 Plastic 5 Correctly placed Incorrectly placed 2 3 4 4 4 4 What is the probability that a randomly selected bottle is correctly placed given that the bottle is made of plastic 2 Simplify any fractions

Solve y 4y 5y 4xe sin x 7cos x by the method of undetermined coefficients

You create a container by rotating the curve y 5 ln x 2 for y 0 to y 3 around the y axis You then fill the container to a height of 1 meters with a liquid that has density 900 kg m The work required to pump the liquid out of this container over its top edge is Joules Recall that acceleration due to gravity is 9 81 m sc0 1

Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x axis X 12y 6y x 0 V

Given the graph of function f below which is greater N 3 off ar da is greater of f x de is greater Othey are the same d Explain in detail why you chose this answer S 2 dx or 2 dz f x dx

Use mathematical induction to prove that the statement holds for all positive integers a 2 4 6 2n n n b 6 10 14 4n 2 n 2n 4

Savings Account The table below shows the December balance in a simple interest savings account each year from 1996 to 2000 Year 1996 1997 1998 2000 1999 Balance 18 000 20 016 22 032 24 048 26 064 a The balances form an arithmetic sequence What is d b Write a formula for the balance in the account years after December 1996 e Find the sum of the December balances from 1996 to 2006 inclusive

3 Express the rational number as a fraction of integers

Use the method of cylindrical y 4 x y 0 shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis x 1 about x 3

P QUESTION 2 Explain why the graph shown is not the graph of y 6 x 3 7

2 points Let f x f x 4 8x 4 8x f x

Determine whether the following quadratic function has a maximum or a minimum value Then find the maximum or minimum value and where it occurs G x x 4x 1 Select the correct choice below and fill in the answer boxes to complete your choice Simplify your answers OA The function has a minimum value of OB The function has a maximum value of at x CELLO at x

me x and y are functions of t Evaluate an exact answer in simplified form dy dt dx for 4xe 12 In 729 6In x with the conditions 12 x 3 y 0 dt

5 4 3 b 16 1 C 5 d 4 XX 2 4 The plot above is created with the parametric equations x t a cos bt ly t c sin dt To acheive this graph a 6

Use the given information Focus parabola 83 7 Ox 2 y 7 8 Ox 3 y 9 2 Ox 2 y 5 3 Ox 3 v 5 1 Directrix X 65 8 to write the equation of the

Use the given information Center 0 8 Radius 5 to write the equation of the circle O x y 8 2 5 O x y 8 2 25 O x y 8 25 O x 8 y 25

elect the an 13 A rock is thrown downward from the top of a cliff with an initial velocity of 3 feet sec Remember the acceleration of a falling object is 32 ft sec Select the function that describes the relationship betwee the velocity v of the rock and time 1 A D v 16t 3 v 321 B E v 32 v 16t 3t C v 32r 3

A tennis ball is thrown downward with an initial velocity of 10 feet sec from the top of a cliff Remember the acceleration of a falling object is 32 ft sec Select the function that describes the relationship betweer the distance the ball travels d and time 1 A d 161 10r D d 32 B E d 161 10 d 16t C d 321 10

11 Given g x 2x 96x and g x 6x 96 select the local maximum and minimum of g x 86 A Local Max 4 0 Local Min 4 0 C Local Max 4 256 Local Min 0 0 E Local Max 0 0 Local Min 4 256 B Local Max 4 256 Local Min 4 256 D Local Max 4 236 Local Min 4 236

dv 2 Given v x x 12x 36x 9 and d 3x 24x 36 select the local maximum and minimum of v x dx A Local Max 6 873 Local Min 2 137 C Local Max 6 9 Local Min 2 23 E Local Max 6 873 Local Min 2 137 B Local Max 2 137 Local Min 6 9 D Local Max 6 873 Local Min 2 23

Find the slope of the tangent line at the labeled point in each graph below 9 86 x 4 10 20 y x 10 86 2 10 y 2x x 1

6 85 f x 8x A f 4x df 4x dx D B f x 16x E f 16x

Select the derivative of each function below 5 85 h x 10x A h x 10x dh x D dx 10 B E h x 0 h 10 C h 5x

At a restaurant the density function for the time a customer has to wait before being seated is given by f t 2e if t 0 if t 0 Find the probability that a customer will have to wait at least 5 minutes for a table

Jump to Problem 1 2 3 4 5 6 7 8 Problem 1 1 point Find the value of k so that the function is a density function Give your answer as a decimal rounded to 6 decimal places k f x kx if 0 x 10 otherwise

1 0 0 8 0 6 0 4 0 2 Y ii Numerically using a right Riemann sum with n 5 You can use the graph of 2xe below 0 2 0 4 0 6 0 8 1 0 x 0 2X0 2 0 2x 0 4 0 2 x 0 6 0 2x0 8 0 2 x 0 8 0 2 x 2 8 0 56