Application of derivatives Questions and Answers

Determine the volume of the solid obtained by rotating the region bounded by y x and x y about the x axis 16T 133 18

Find the derivative of the function f x f x X ex

Find the derivative of the function f x 5e f x 5 1

Listen Use differentials and the volume of a sphere to estimate the amount of paint needed to apply a coat of paint 0 18 cm thick to a hemisph rical dome with a diameter of 50 meters 2 28 m 3 2 52 m 3 82 m 3 2 25 m 04 11 m

Listen Determine the linear approximation function L x forf x tan x when a 0 OL x x 1 tan x x 1 when x is near zero OL x x 1 tan x x 1 when x is near zero OL x 1 tan x 1 when x is near zero OL x x tan x x when x is near zero OL x 1 tan x 1when x is near zero

Determine the differential for y 10 tan 10 tan t O dy O O dy dy 5sec t t 5sec t t dt dt 5sec t t 10sec t dt d

The total cost of producing a type of truck is given by C x 22000 40x 0 05x where x is the number of trucks produced How many trucks should be produced to incur minimum cost Answer Keyp

Among all rectangles that have a perimeter of 162 find the dimensions of the one whose area is largest Write your answers as fractions reduced to lowest terms Answer Ke Keyboard She

Among all rectangles that have a perimeter of 180 find the dimensions of the one whose area is largest Write your answers as fractions reduced to lowest terms Keypa

Find a formula for the quadratic function depicted in the following graph 10 5 Ay 10 5 Enable Zoom Pan 5 10 X

Use a line integral on the boundary to find the area of the following region A disk of radius 14 Set up the integral needed to find the area using the standard parameterization for a circle Use t as the independent variable 2T 0 7 dt Type exact answers using as needed

The average cost of a turntable is given by C x 140 000x 30 0 02x dollars per turntable Wee production is currently 3 000 and is increasing at a rate of 120 turntables per week A What is the average cost of producing 3000 boats B How is the average cost changing per week Is it increasing or decreasing dC d Hint Find when x 3 000 and dx 120 de

Find the surface area of revolution about the x axis of y 5 sin 3x over the interval 0 x

olve the triangle Bound to ono decimal place as needed 4 B C 5 2 A

For what numbers x 21 x 2 does csc x 1 Refer to the graph which shows y csc x in blue and y sin x in red In the interval 2x x 2 what is the smallest value of x for which cscx 1 3r 2 Type an exact answer using as needed Use integers or fractions for any numbers in the expression Simplify your answer Within the given interval what is the next x value for which csc x 1 IN

ketch a graph of a function f that is continuous on and has the following properties f x 0 and f x 0 on 1 f x 0 and f x 0 on 1 00

For what numbers x 2 x 2 does cscx 1 Refer to the graph which shows y csc x in blue and y sin x in red In the interval 2 x 2 what is the smallest value of x for which csc x 1 B Type an exact answer using as needed Use integers or fractions for any numbers in the oxproccion Simplifi

1 point The height in centimeters of the tip of the minute hand on a vertical clock is a function f t of the time t in minutes The minut hand is 24 cm long and the middle of the clock face is 296 cm above the ground a The midline of the graph of f t is y include units help units b The amplitude of the graph of f t is include units help units

Find the arclength of y 4x 2 on 4x 2 on 2 x 4

Compute the discharge over the sharp crested weir shown below b 0 32m y 0 12m and weir height h 0 55m Solution 1 Discharge coefficient Cd 0 62 18 2 Effective width due to end contraction 2 sided beffective 3 Discharge over the weir Q 0 0237 m s m contracted m

The volume of air contained in the lungs of a certain athlete is modeled by the equation U 329 sin 83zt 817 where t is time in minutes and u is volume in cubic centimeters What is the maximum possible volume of air in the athlete s lungs Maximum volume cubic centimeters What is the minimum possible volume of air in the athlete s lungs Minimum volume cubic centimeters How many breaths does the athlete take per minute breaths per minute

1 point Find a formula for the trigonometric function graphed below Use x as the independent variable in your formula f x help formulas I 8 5 6 25 8 25 8 5 pi 12 Click on graph to enlarge pi 6

1 point Find amplitude and midline of the function y 8 cos 4x 3 a The midline is the line with equation b The amplitude is help numbers help equations

1 point Find the midline and amplitude of the graph of the blue function a The midline of the graph is the line with equation equations b The amplitude of the graph is help numbers help 6 2 1

A projectile is launched upward with a velocity of 160 feet per second from the top of a 70 foot platform What is the maximum height attained by the projectile height functions Answer How to enter your answer opens in new window Keypad

Among all rectangles that have a perimeter of 248 find the dimensions of the one whose area is largest Write your answers as fractions reduced to lowest terms Answer Keyp

Maximize the utility function U x y xy subject to the budget constraint 5x 9y 30 and find the maximizing value of y Round your answer to the nearest one decimal place e g 13 14 rounds to 13 1 and 13 15 rounds to 13 2 You can attach your work to support your answer

Step 2 of 2 Use the quadratic formula f x 3x 18x 23 to determine the coordinates of the vertex of the best fitting parabola Write the exact answer Do not round Answer h k Keypad Keyboard Shortcuts

6 The function f x x cos x has a zero p 0 7390851332 Let po 5 and P 5 Set the tolerance equal to 10 10 for the Bisection method Newton s method and the Secant method Rank these methods according to the number of steps needed to achieve the desired tolerance

Use the polygon to the right to complete parts a and b a Name the polygon If the polygon is a quadrilateral give its specific name b State whether or not the polygon is a regular polygon a What is the name of the polygon O Hexagon O Dodecagon O Pentagon Square Is the polygon regular or not regular

Hurz f6 In x x b arc where a b c constants Find f all

Find the F x 5x 6 derivative Suet de

Problem 4 20 points Consider the set of all rectangles that lie in the first quadrant have one edge along the positive x axis one corner at the origin and the diagonally opposite corner on the curve y e Find the dimensions of the rectangle in the set that has the largest area

se the matrices he total revenue for each booth Quantity Sold Booth 1 below to determine Booth 2 Shirts Hats Decals 70 90 85 100 50 90 otal Revenue for Booth 1 Shirts Decals otal Revenue for Booth 2 Hats Price 10 8 7

The lifting force F exerted on an airplane wing varies jointly as the area A of the wing s surface and the square of the plane s velocity v The lift of a wing with an area of 250 square feet is 13 400 pounds when the plane is going at 200 miles per hour Find the lifting force if the speed is 140 miles per hour Round your answer to the nearest integer if necessary Answer Keypad Keyboard Shortcuts

The average cost of a turntable is given by C x 140 000x 1 30 0 02x dollars per turntable Weekly production is currently 3 000 and is increasing at a rate of 120 turntables per week 1 What is the average cost of producing 3000 Jet Skies

a varies directly as b and inversely as the cube of c If a 105 when b 4 and c 4 find a if b 10 and c 9 Round your answer to two decimal places if necessary Answer Keyp Keyboard Short

Determine the value of a b 2 3 1 1 2 4 1 3 a 4 b a 1 C 1

Determine the value of x 12 24 2 1 1 3 4 8

Determine the number of ways each procedure can be done Line up three people for a photograph Prioritize four pending jobs from most to least important Arrange five books from left to right on a bookshelf Award ribbons for 1st to 5th place to the top five dogs in a dog show

A multiple choice test consists of 5 questions with each question having 3 posible answers How many differ

Two hallways one of width 2 feet the other of width 6 feet meet at a right angle See the illustration Complete parts a through d A L 0 2 sec 0 6csc0 OB L 0 2 csc0 6 sec 0 OC L 8 2 cos 8 6 sin 0 OD L 8 2 sin 0 6 cos 0 b Graph L L 0 0 0 2 A Q All graphs are by 0 28 For what values of 8 is L the least B G O C O D

2 f x x 3x f derivative f x to Ure the definition find f x f x and

The graph of y 2x 4 X 5 has a vertical asymptote What is it

T Find the average rate of change of f from 0 to 12 f x tan 2x The average rate of change is Simplify your answer including any radicals Type an exact answer using as n

Find the gradient function for p x y ysin z 48 1 2

Plot the following points on the graph on the right Label them with the A B C corresponding to the parts A B and C respectively 2 pts each A B 5 17 p c 2 77 51 6 31 71 6 51 4 2 41 31 2 F M templa 71 6 6 0 11 6

A bridge is supported by triangular braces If the sides of each brace have lengths 63 feet 46 feet and 40 feet find the measure of the angle opposite the 46 foot side

Find the work done by a force of 5 pounds acting in the direction of 60 to the horizontal in moving a box from the point 0 0 to the point 20 0 10 pts

g v 1 3 2 and Find the cross product of 1 4 5 and w 6 pts