Differentiation Questions and Answers

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at t 0 at t 00 Decay of current In state when steady state is achived do E R Loli jR 0 dat Loi dit i o i io to steady state J A R di iR L H T r i Ti R L mum t dt R mor R 7 J ve sign represents a will dicrease with ata

Police use the formula v 20L to estimate the speed of a car v in miles per hour based on the length L in feet of its skid mark when suddenly braking on a dry asphalt road At the scene of an accident a police officer measure a car s skid marks to be 100 feet long Approximately how fast was the car traveling Round your answer to the nearest tenth one decimal place of a unit Answer The car was traveling at approximately miles per hour

Tell whether each sentence below is true or false 1 The secant y sec x and cosecant y cscx functions have no x intercepts zeros 47 2 A trig equation can have more than one solution 50

Achild standing 4 feet away from his mother lets go of his balloon at the same height as his mother s line of sight The balloon is rising at a rate of 1 foot per second How fast is the angle of elevation from the mother to the balloon changing 3 seconds later

1 Consider the function f z on the interval 4 8 Find the average or mean slope of the function on this interval By the Mean Value Theorem we know there exists a c in the open interval 4 8 such that f c is equal to this mean slope For this problem there is only one c that works Find it

If we apply Rolle s Theorem to the function f z 2z 20z 3 on the interval 3 7 how many values of c exist such that f c 0 What is the value of c If we try to apply Rolle s Thorem to the function f x 2x 20z 3 on the interval 0 14 which of the following conditions is not met O differentiability on 0 14 Of a f b O continuty on 0 14

Find the maximum and minimum values of the function g 0 40 9 sin 0 on the interval 0 Minimum value Maximum value Question Help QUE

Consider the function f x 4x 6x 3 0 1 7 The absolute maximum of f z on the given interval is at z and the absolute minimum of f z on the given interval is at z

Consider the function f z 6x 4z 1 f z has a critical point at z A Find the value of A A At z A does f z have a local min a local max or neither Type in your answer as LMIN LMAX or NEITHER

and for fy f x y 10 4x 7y 8 f x x y l

If y t 6t 8 2 4 find dy dt Questing Wale e dy dt

Find the slope of the tangent line to the curve 3x 2xy 1y 92 at the point 2 4

Question 20 Consider the function f x exact values f x f x x 3x 1 Compute each of the following Simplify your answer and use I 1

Textbook y cos z 4 dy dz Find dy dz Type sin x for sin z cos x for cos z and so on Use x 2 to square x x 3 to cube x and so on Use sin x 2 to square sin x Do NOT simplify your answer

Textbook Videos Use the chain rule to find the derivative of f z 5 10z 4z 6 You do not need to expand out your answer f x Question Help Video

The accompanying table is from a study conducted with the stated objective of addressing cell phone safety by understanding why people use a particular ear for cell phone use The goal was to determine whether the ear choice is associated with auditory or language brain hemispheric dominance Assume that one wants to test the claim that handedness and cell phone ear preference are independent of each other Complete parts a and b below P Right Handed Left Handed Right Ear 447 19 Because Left Ear 179 50 No Preference 37 2 a Use the data in the table to find the expected value for the cell that has an observed frequency of 2 The expected value is Round to three decimal places as needed b What does the expected value indicate about the requirements for the hypothesis test the requirements for the hypothesis test satisfied EXOD

Five data entry operators work at the data processing department of the Birmingham Bank Each day for 30 days the number of defective records in a sample of 300 records typed by these operators has been noted as follows a Establish 30 upper and lower control limits UCL Sample No LCLp b Why can the lower control limit not be a negative number 1 2 677494556 10 No Defectives 8 4 20 10 12 8 13 9 7 14 Sample No 11 12 13 14 15 16 17 18 19 20 No Defectives 7 5 16 3 11 9 11 5 18 15 enter your response as a number between 0 and 1 rounded to three decimal places enter your response as a number between 0 and 1 rounded to three decimal places Sample No 21 22 23 24 25 26 27 28 29 30 OA Since the percent of defective records cannot be a negative number B Since the upper control limit cannot be a negative number C Since the percent of defective records is always a positive number OD Since the upper control limit is positive c The industry standard for the upper control limit is 0 10 What does this imply about Birmingham Bank s own standards The industry standard is the standard at Birmingham Bank No Defectives 16 11 6 6 14 10 14 5 11 3

OOK Videos If f z 6 tan 4 sin 3x f x Question Heln

If f x f x COS 526 find f x Use exact values

If f x sin 5x find f x Use exact values f x

Write each product as a sum containing only sines or cosines Select the choice that matches your answer 2B 4B 3 22 sin COS 3 57 A D 1 D sin 2 1 2 A 0 COS 23 cos 30 cos 50 57 2 3 2 3 1 2 1 2 4 3 COS cos 2 cos 20 cos cos 80 B E B E 2 cos COS 1 cos 28 cos2 3 2 1 sin 2 8 sin 25 2 3 cos 30 cos 50 1 1 cos 30 cos 50 2 C C 2 sin 20 sin 1 cos 20 cos 80

Textbook Find the derivative of f x 10x 4z Videos Question Help Video

Two vehicles start out traveling side by side along a straight road Their position functions shown in the following graph are given by s f t and s g t where s is measured in meters and t is measured in seconds 10 9 8 7 6 2 1 f t Which vehicle has traveled farther at t 2 seconds B Vehicle f Vehicle g What is the approximate velocity of the f vehicle at t 3 seconds meters per second What is the approximate velocity of the g vehicle at t 3 seconds meters per second Which vehicle is traveling faster at t 4 seconds Vehicle f

Twice a positive integer squared less 3 is What is the integer A S B 7 C 11 D 13

Complete the lowing a The graph of y g x is shown Draw the graph of y g 2x 1 K 8 6 4 2 8 6 at 2 2 4 6 8 2 4 56 100 3 x X

9 Find the reference angle for 312 a 132 b 48 c 48 d 21

3 Solve the trig equation 2 sin 3x 1 0 2 a x 1 1 277 4 6 3 2n 99 9 b x C X d x TT 5T 2n 18 18 3 5 9 2n 6 3 9

solve by power serise the following DE N 31 N T

B 1 5 6 7 8 9 10 11 12 13 14 15 A B C D E d da f x g x f x g x g x f x a For each of the following functions use the Product Rule to find the function s derivative Be sure to label each derivative by name e g the derivative of g x should be labeled g x i g x x sin x ii h x xe iii p x x ln x iv q x x cos x v r x e sin x iii 3 b Use your work in a to help you evaluate the following indefinite integrals Use differentiation to check your work i fx ex e dx ii fe sin x cos x dx F

Use the properties of logarithms to expand log Each logarithm should involve only one variable and should not have any exponents Assume that all variables are positive log 0 9 N log X 3

Find the derivative of f t t4 t5 1 t6 f t Plot the graphs of f t and f t together on the same plot to check your result

The Fresnel function which has applications in optics and highway design among other areas is defined as as an integral accumulation function S a sin 7 2 dt Determine the x coordinate s of the local maximum maxima on 3 x 3 List all of these values in increasing order If any blanks are unused type N in the corresponding blank X X C X X X

Fourier sine transform of f x e is O 1 1 q O 2 O XX 1 a O 1 a X 1 a 2 1 q

22 Find the point that corresponds with a b 0 1 c 1 13 2 d 3 1 4T 3

21 Find the magnitude and direction of the vector 5 4 a Magnitude 3 Direction 39 b Magnitude 41 Direction 141 c Magnitude 41 Direction 321 d Magnitude 3 Direction 123

15 Find the amplitude and period of the equation y 2cos3x a Amplitude 2 Period 3 b Amplitude 2 Period 2 t 3 c Amplitude 3 Period 2 d Amplitude 3 Period

5 Approximately how many feet tall is the streetlight a 12 8 b 15 4 c 16 8 d 23 8 h 20 ft 40

7 Find the reference angle for 129 a 309 b 51 c 51 d 39

nd and simplify the difference quotient x h f x for the function f x x 3x 5 h

What is the maximum perimeter of a right angle triangle with a hypotenuse of 12 cm a 24 cm Ob 24 2 cm Oc 12 12 2 cm d 12 2cm

Find the derivative of the given funciton f x x tan x a f x 2x sec x O b c f x f x d f x 2 X tan x 2xtan x x sec x tan x 2x c0c2 x

etermine two coterminal angles in radian measure one positive and one negative for each angle There are many correct answers Enter your answers as a comma separat a b 7 rad 3A 2 47 8 3 5 A 8 3R 2 0 0

A conical tank has a height 5 m and a radius 2 m at the base Water flows at a rate of 2m 3 min How fast is the water level rising when the level is 1 m and 2 m When the water level is 1 m the water level is rising at a rate of When the water level is 2 m the water level is rising at a rate of I found for 1m 3 977 and another try 1 91 2m 0 994 another try 0 48 non of those answers

Let w a x y z dx b x y z dy c x y z dz be a differentiable 1 form in R such that dw 0 Define f R R by L aux a tx ty tz x b tx ty tz y c tx ty tz z dt f x y z Show that df w

The twist angle x t of a torsionally vibrating shaft of unit length is determined from 8 0 2x where An 1 S 1 Then 0 x t An cos a n 0 5 t sin n 0 5 x n 0 dx 22 dx a 0 0 t 0 8 0 t2 0 x 1 t 0 20 dr 0 x 0 x x 2 x 1 0 t 0 20 t It 0 0 t 0

81 Let f x 0 if x is any rational number and f x 1 if x is any irrational number Show that f is not integrable on 0 1

5 The polar coordinates of a point are given Find the rectangular coordinates of the point how 5 2 4 a 6 c d 2

For the matrix B shown below determine the value of the element b12 If the element is not defined click the undefined button 5 8 B 6 1 6

Given the definitions of f x and g x below find the value of f g 0 f x x 4 g x 3x 7x 8