Application of derivatives Questions and Answers

Solve the equation 2 3 1 5 X Question 1 Select the correct choice below and

3 Evaluate t 1 In t dt 2 1 1 In 1 1 1 C a t 1 n 1 1 C 4 d b 2 1 In 1 P 1 t t 1 In t 4 t C

Evaluate sinh 2ln 3 a 40 9 c 9 b d 0 41

3 2 1 1 2 3 2 4 4 How many non zero rows does RREF A have Does the equation AX b have a solution for all b E R Do the columns A span R

Zoom DIVI Need Help Zoom Divi XVMAT 125 Sp webassign net web Student Assignment Respons Read It

If a ball is thrown into the air with an initial velocity of 48 ft s its height in feet after t seconds is given by y 48t 16t a Find the average velocity of the ball in ft s for the time interval beginning at t 2 and lasting for each of the following 1 0 5 seconds 40 1 0 1 seconds 17 6 ii 0 05 seconds 16 8 iv 0 01 seconds 16 16 X ft s X ft s X ft s Bond X ft s b Use your answers from part a to estimate the instantaneous velocity in ft s when t 2 16 X ft s Enhanced Feedback Please try again When calculating the average velocity you are actually calculating the slope of the secant line between the two given points difference in height between the given times and divide by the change in time To estimate the instantaneous velocity look at what the average velocity approaches as the time difference gets smaller Need Help

x y 5x xy y5 approximate fy 3 2 using Ay 0 01 Round your answer to two decimal places f y 3 2 approx

Find the center of mass of a thin plate of constant density covering the given region The region bounded by the parabola y 6x 3x and the line y 6x The center of mass is 12 Type an ordered pair

Find the amplitude and period of the function y cos x amplitude period Sketch the graph of the function y 0 3 0 2 0 1 0 1 0 2 0 3 y 44 0 3 0 2 0 1 0 1 02 9 5 5 1 0 10 1 5 15 2 0 X y 3 2 1 1 2 y 0 3 0 2 0 1 0 1 5 10 10 15 15 M

y sin 3x amplitude period Sketch the graph of the function y y 3r 1 3 0 5 2 A A 3 2 6 3 2 0 3L y 3 312 1 312 KIN 2 3A 2 3 T 2 X 2 X 2 0 5 1 y 1 0 5 LA 0 5 996 T 2 513 KIN 3 2 2 3

hree regions are defined in the figure C 0 3 y 0 R y 3 x R3 y 3 x R B 1 3 A 1 0 X ind the volume generated by rotating the given region about the specified line about AB

This calcium salt contains an anion with 18 electrons onic compounds are sometimes called salts O CaAr O CaCl O Cas

6 Center at 4 5 and tangent to the y axis 71 D x 4 y 5 16 x 4 y 5 25 B x 4 y 5 16 E x 4 y 5 4 C x 4 y 5 25

The graph of one complete period of a sine curve is given y period 3 4 horizontal shift 8x 3 a Find the amplitude period and horizontal shift Assume the absolute value of the horizontal shift is less than the perio amplitude X b Write an equation that represents the curve in the form y a sin k x b

ven that lim f x 0 x a b lim g x 0 x a c lim p x 00 X a valuate the limits below where possible If a limit is indeterminate enter INDETERMINATE a lim f x p x x a lim p x g x x a lim h x 1 x a lim p x g x x a lim q x 00 x a

company introduces a new product for which the number of units sold S is given by the equation below where it is the time in months S t 335 3 2 a Find the average rate of change of S t during the first year b During what month of the first year does S t equal the average rate of change April

Omar wants to use a graph to solve the equation below logs x log x 4 Which system of equations should Omar use log6 Y2 X log2 X 4 O Y O 15 0 OY logx log6 log6 log2 logx log6 Y2 logx 4 log2 log x Y2 log x 4 Y2 log x 4 log2

Which function is shown in the graph below TITT CONCO 4 10 8 6 4 2 2 4 4 9 8 1537 B 8 10 x

What is the value of log6255 O 4 14 K 4 04

The range of which function is 2 00 O y 2x O y 2 5 O y 5x 2 O y 5x 2

The intensity or loudness of a sound can be measured in decibels dB according to the equation dB 10log where I is the intensity of a given sound and is the threshold of hearing intensity What is the intensity in decibels dB when 10 08 O9 19

sample of a radioactive substance decayed to 92 of its original amount after a year Round your answers to two decim aces a What is the half life of the substance yr b How long would it take the sample to decay to 65 of its original amount yr

roast turkey is taken from an oven when its temperature has reached 185 F and is placed on a table in a room where mperature is 75 F Round your answers to the nearest whole number a If the temperature of the turkey is 150 F after half an hour what is the temperature after 55 minutes T 55 F b When will the turkey have cooled to 100 t min

5 Convert the following vectors 4 marks a 75 m s on a bearing of 295 to Cartesian form b 3 8 to direction magnitude form

hing Piecewise Functions Level 7 16 8 42 35PM Jatch hela ryideo h the following function on the axes provided f x 3x 12 for x 3 1 for x 5 Click and drag to make a line Click the line to delete it Click on an endpoint of a line to change it

BOX E Answer Sheet Word Problems on the following pages Put your answers on this page from choices given Circle your choice only one per question SHOW your calculation set ups on the following pages clearly and with all conversion factors properly labeled with units Show unit cancellation Keep in mind that significant figures are part of the correct answer 1 a 7200 s b 5 6 x 10 s c 2 0 s d 120 s 2 a 0 7 days b 0 6944 days 3 a 333 grains b 0 02 grains c 400 days c 7 5 grains e 5 6 x 10 s d 2 500 days e 2 5 days d 0 8 grains e 3000 grains 4 a 5 59 per mile b 1 00 per mile c 0 18 per mile d 5 55 per mile e 0 01 per mile

9 What mass of mercury density 13 6 g cm will occupy a volume of 25 0 mL

Show that the point is on the unit circle 33 4 We need to show that the point satisfies the equation of the unit circle that is x y 2 33 7 x y 33 49 2 3 Hence the point Select on the unit circle

C Consider the expression AV0 5 1 help you with your calculations AVO 05

t Find t and the terminal point determined by t for each point in the figure where t is increasing in increments of 4 Terminal Point 0 4 4 4 1 X C 2 2

a If we mark off a distance t along the unit circle starting at 1 0 and moving in a counterclockwise direction we arrive at the Select point determined by t terminal b What are the terminal points determined by 2 T 2 and 2 reference quadrant 2 I 2 2 x y x y x y x y

The displacement in meters of a particle moving in a straight line is given by s t 7t 19 where t is measured in seconds A i Find the average velocity over the time interval 4 5 Average Velocity ii Find the average velocity over the time interval 4 5 5 Average Velocity iii Find the average velocity over the time interval 5 6 5 Average Velocity iv Find the average velocity over the time interval 5 5 5 Average Velocity 1 meters per second Quem B Find the instantaneous velocity when t Instantaneous Velocity 5 meters per second meters per second meters per second meters per second

19 32 Amplitude and Period Find the amplitude and period of the function and sketch its graph 19 y cos 2x punim nog 21 y sin 3x 23 y 2 cos 3TX Tomzesi 20 y sin 2x 22 y cos 4TX 24 y 3 sin 6x mon of omarnos

Let g be a continuous function that is one with no jumps or holes in the graph and suppo of y g a is given by the graph shown below 3 3 O 2 7 O 2 10 40 2 O 2 O a Observe that for every value of that satisfies 0 x 2 the value of g x is constant What does this tell you about the behavior of the graph of y g x on this interval Why b On what intervals other than 0 x 2 do you expect y g x to be a linear function Use the interval notation c At which values of x is g x not defined What behavior does this lead you to expect to see in the graph of y g x 3 2 5 3 1 0 2 1 2 2 5 2 d Suppose that g 0 1 On the axis provided sketch and accurate graph of y g x 3 2

If y 1 3 X dy find at x 2 dx The value of dy dx Simplify your answer at x 2 is

31 3 2 1 2 the intervals where the derivative of this graph is positiv al notation erivative on the interval s erivative on the interval s

ore 1 13 0 16 answered Question 6 Use the graph of f x below to find the following derivatives Write DNE if the derivative does not exist but 3 You can zoom in using the magnifying glass in bottom right corner of graph f 6 f 0 f 2

Homework 1 3 1 4The Derivative of a Score 1 5 13 0 16 answered Question 8 Y The figure below shows a function p x and its tangent line the tangent line is 5 75 3 19 fill in the blanks below to at the point B

n Get a similar question 14 12 10 8 6 4 for more 2 You can retry this qu a Mark the two poin needed to calculate the interval 5 4 b Connect the point c The Average Rate Opositive O negative

63 70 Using the Pythagorean Identities Find the values of the trigonometric functions of t from the given information 63 sin t terminal point of t is in Quadrant IV 59

circle in the figure 1 Let P x y be the terminal point on the unit circle deter 7 4 in Exercise 4 t increases in increments of 6 See Exer cises 21 and 22 in Section 5 1 mined by t Then sin t 3 and tant 2 If P x y is on the unit circle then x y So for all t we have sin t cos t COS SKILLS 3 4 Evaluating Trigonometric Functions Find sint and cost for the values of whose terminal points are shown on the unit 1 1 1 7 x 4 t x

5 22 O Evaluating Trigonometric Functions Find the exact value of the trigonometric function at the given real number 5 a sin 7TT 6 17T 6 b cos c tan 7TT 6

23 36 Terminal Points Find the terminal point P x y on the unit circle determined by the given value of t 24 t 3 23 t 4 81HOUR GW

The curve y is called the witch of Agnesi after the Italian mathematician Maria Agnesi 1718 1799 who wrote one of x 1 the first books on calculus This strange name is the result of a mistranslation of the Italian word la versiera meaning that which turns Find equations of the tangent lines to the curve at x 6 Use symbolic notation and fractions where needed At x 6 the tangent line is y At x 6 the tangent line is

To determine drug dosages doctors estimate a person s body surface area BSA in meters squared using the formula hm BSA where h is the height in centimeters and m the mass in kilograms 60 Calculate the rate of change of BSA with respect to mass for a person of constant height h 182 Give your answer exactly using symbols Do not approximate irrational numbers with decimals for this part of the problem d dm BSA What are the units for Om kg O m O cm kg O kg d dm BSA For a person of constant height h 182 cm how fast is their BSA changing when their mass is m 72 Use decimal notation Give your answer to six decimal places

Question 3 0 5 points Listen Two sides of a triangle are 2 m and 3 m increasing at a rate of 0 07 rad s Deter triangle is increasing when the angle be 00 105 m s 05 045 m s

A particle moving along a line has the position s t 521 m at time t seconds At what time t for t 0 does the particle pass through the origin Give your answer to three decimal places At what time t for t 0 is the particle instantaneously motionless i e it has zero velocity Give your answer to three decimal places S

The dollar cost of producing x bagels is C x 300 0 25x 0 4 0 1000 Determine the cost of producing 4000 bagels Use decimal notation Give your answer to one decimal place C 4000 Estimate the cost of the 4001st bagel Use decimal notation Give your answer to three decimal places The estimated cost of the 4001st bagel is Find the actual cost of the 4001st bagel Use decimal notation Give your answer to three decimal places The actual cost of the 4001st bagel is

By Faraday s Law if a conducting wire of length meters moves at velocity v m s perpendicular to a magnetic field of strength B in teslas a voltage of size V v Blu is induced in the wire Assume that B 3 and 0 6 dV Find the rate of change du Use decimal notation Give your answer to one decimal place dv du Find the rate of change of V with respect to time t if v 9t 9 Use decimal notation Give your answer to one decimal place dV dt

The power delivered by a battery to an apparatus of resistance R in ohms is P R power with respect to resistance for R 69 Use decimal notation Give your answer to four decimal places The rate of change is approximately 2 4R W Find the rate of change of R 0 5 W S