Application of derivatives Questions and Answers

Discuss the continuity of the function Enter your answers as a comma separated list 9 x 3 f x f is discontinuous at x y 7 T 6 5 4 3 X 7 6 5 4 3 2 11 1 2 3 4 5 6 7 2 1 2 3 IN III 6 7 4 5

Sum and Difference Formula sin A B sin A cos B sin B cos A sin AB sin A cos B sin B cos A cos A B cos A cos B sin A sin B cos AB cos A cos B sin A sin B b sin 0 sin 0 2 0 Value 3 Double Angles sin20 2sin Occ 1 Find the general solution to the following equations a tane 3 Value 2 a cos 20 1 0 Value 3 cos 20 cos 2 cos 1

Find the absolute extrema of the function f x y 4x 2 4y 2 3x 3y 2 on the domain defined by x 2 y 2 25 Round answers to 3 decimals or more Absolute Maximum Absolute Minimum

Consider the following piecewise defined function 2 3 4 40 5 x 8 Step 1 of 3 Evaluate this function at x 2 Write the exact answer Do not round If the answer is undefined write Und as your answer Answer f x ifx 3 ifx 3 f 2

3 A truck travelling north east at 80km h is 250km south east of a sports car headin South east at 130km h what will the minimum distance between them be

Sum the values of f x 9x 5x 7 evaluated at x 1 07 x 1 17 x 1 27 x 2 77

Tom invests 7500 00 for 6 years at 4 per annum compounded monthly How much does he have at end of the 6 years

Stefan cashed a 1956 simple interest CSB with an annual rate of 5 He received 803 in interest during the time he held the bond How long did he hold the bond in years Round your answer to 1 decimal place For instance if it is 10 231 years then your answer would be 10 2 years

A term deposit of 4 months at 4 per year paid 73 simple interest on maturity Calculate the principal invested Round your answers to 3 decimal places For example if your answer is 500 2314 round to 500 231

Use Interval notation to write the Intervals over which fis a increasing b decreasing and c constant Part 1 of 3 y f x The function is never increasing O The function is sometimes increasing Increasing interval O The function is always increasing Increasing interval Part 2 of 3 The function is never decreasing The function is sometimes decreasing Decreasing interval 0 0 00 DVD X 0 0 00 GUC 00 G 00

sin x z0r f x and lim g x 16 what could f 0 and g 0 be Justify your solution 2 0 9 Suppose f and g are two functions continuous at x 0 If lim 2 1 f x 0

4 Use the graph shown to evaluate lim 1 1 g x g g x y 2 5r 2 5 v f x

f x 2 0 g x 3 Use the graph shown to evaluate lim y g x

1 Suppose f x and g x are differentiable at r 0 and f x and g r are continuous at r 0 If f 0 g 0 0 f 0 5 and g 0 3 evaluate the limit tan x 4 0 g sin x lim

5 lim tan 2 0 6 lim In 2x sin x sin x x 4x 3 2x 3

1 Determine a and b is such a way that the following function is continuous at z 1 Justify yo solution f x 001 8 a tan bx x 1 bx 4 Community Ca if r 1 if x 1 if r 1

Let f x r2 52 6 4 x a Find lim f x If the limit does not exist explain why x4 2 b Find lim f x If the limit does not exist explain why c Based on your work in parts a and b does the graph of f x have any vertical asymptotes If so find the equations of the vertical asymptotes d Find lim f x and lim f x x 8118 e Based on your work in part d does the graph of f x have any horizontal asymptotes If so find the equations of the horizontal asymptotes of f x

Suppose the curren exchange rate for united state to Indian rupees is 69 82 rupees equals If maneet is returning to India to vist family and brings 250 How much Will She receive in rupens money

In AEFG e 8 9 cm f 7 7 cm and g 2 2 cm Find the measure of ZF to the nearest degree

In ASTU t 34 cm u 16 cm and ZS 56 Find the length of s to the nearest centimeter

c Find the local maximum and minimum values of the function g x X

Local Minima and Maxima a Find the local maximum and minimum values of the function f x x 3x 9x 5

5 Island A is 280 miles from island B A ship captain travels 340 miles from island A and then finds that he is off course and 170 miles from island B What angle in degrees must he turn through to head straight for island B Round answer to two decimal places a 124 88 d 34 88 b 55 12 c 69 75 6 Find the area of the triangle with a 32 b 7 and c 5ft Round your answer to two decimal places b 14 84 ft a 18 55ff c 9 27 ft d 17 50 ft

Intervals crease ar ease a Find the intervals on which the function f x x 6x 9x 1 is increasing or decrea

b Find the critical points of the function f x x2 x 2

A rocket is launched so that it rises vertically A camera is positioned 5000ft from the launch pad When the rocket is 1000ft above the launch pad its velocity is 600ft sec Find the necessary rate of change of the camera s angle as a function of time so that it stays focused on the rocket

A company determines that its weekly online sales S t in hundreds of dollars t weeks after online sales began can be estimated by equation below Find the average weekly sales for the first 4 weeks after online sales began S t 6et The average weekly sales amount is 2862040 55

b Two airplanes are flying in the air at the same height airplane A is flying east at 250 mi h and airplane B is flying north at 300mi h If they are both heading to the same airport located 30 miles east of airplane A and 40 miles north of airplane B at what rate is the distance between the airplanes changing

dz dx a Find at x y 1 3 and z x y if dt dt 4 and dy dt 4

Consider the following piecewise defined function 3 x 4 2 32 X 8 Step 2 of 3 Evaluate this function at x 4 Write the exact answer Do not round If the answer is undefined write Und as your answer Answer f x f 4 if x 4 7 if x 4

The following diagrams are ray diagrams showing how to locate the image On GREEN of an object arrow On REC Diagram A Diagram B Diagram C the he fee Which of these diagrams are correctly drawn Select one O A Ob B Oo All of these 21

Use the elimination method to find all the solutions of the follow system of equations 3 The solutions from left to right are 1 where where and y 2 and y and 2 92

Solve 2x 20x 8 by completing the square Show all steps For the toolbar press ALT F10 PC or ALT FN F10 Mac

Two similar looking series are given Test each one for convergence or divergence n a 2 n 1 b O convergent O divergent n 1 n 2 2 2 2 O convergent O divergent

mswer each question below 22 What is the maximum number of turning points that the graph of m x 4x x 6x 9 can have 12 then what does 0 equal

ne of the following limits requires algebraic simplification to evaluate while the other does not Decide which is which and evaluate them b lim 1 2 In x 1 lim x 3 x 3 2 x 16 5

The problem requires a calculator that can evaluate logs Using the model N 300 2 for bacteria growth where is measured in 20 minute time periods how long will it take for the bacteria count to reach 36 000 Give your answer in minutes not in 20 minute time periods and round the answer to two decimal places It takes approximately 1 minutes for the bacteria count to reach 36 000

3 Finding the average value of a linear function Find the average value of f x 7x 1 over 3 8 average value Activate

The family Arts 22 Per adult and 113 per Senior Citizen 4199 people paid the total was 7927 how many Senior Citizens no

2 1 0 x 0 2 2 x models the A 20 apple juice drink is mixed with a 100 apple juice drink The function f x concentration of apple juice in the drink after a gallons of the 20 drink are added to 2 gallons of pure juice What will be the concentration of apple juice in the drink if 6 gallons of 20 drink are added Give the answer as a percent but do not include the percent sign

ESTION 3 Find the compound amount for the deposit Round to the nearest cent 6000 at 10 compounded annually for 5 years 9000 00 8400 00 8784 60 9663 06

Jox he toolbar press ALT F10 PC or ALT FN F10 Mac ste the integral dx Type your soluton in the space provided and show each step you took to solve this problem

2 5 pts 6 3 148 Sketch the region bounded by x y and y x Determine the volume when the region is rotated about the line y 2 44 24

Find max point for f x x 6x 1 1 4 4 6 1 4 4 6 Onone of these answers O 1 4 4 6 Question 8 Give decreasing interval for f x in interval notation f x x 1 5 x 6x 1 2 none of these answers O 2 1 1 2

Solve the given equation and give solutions for x log x 2 log x 1 1 O none of these answers Ox 4 and x 3 O x 3 only Ox 4 and x 3 Question 16 Solve for x 10 x 5 8 60 x 6 83 Onone of these answers x 3 16 x 6 83

find f x h O x 2xh h 3x 3h O x h 3x 3h O none of these answers O x h 3x 3h Question 22 combine into one log expression log x 1 log x 1 log x log 3 Olog x 1 3 x Olog x 1 3x log x 1 x 1 3 x Olog x 1 3 x 352 0002 20 S 12252 254288

g x 21 6 O any number greater or equal to 2 O any number less than or equal to 2 O none of these answers O any number greater than or equal to 1 3 Question 10 Find Equation of Vertical Asymtotes g x 3x 2 x x 6 0x 3 x 2 0x 3 x 2 Onone of these answers 0x 3 x 2

0 Find domain of this function y log x 2 OX 2 none of these OX 2 O infinity infinity Question 2 Find the x intercept and the y intercepts for the function given below y log x 2 O x 3 is its x intercept and no y intercept Onone of these no x intercept and y 2 is the y intercept x 2 is its x intercept and no

1 Find te 3x dx 0 a diverges c 0 b d

9 A particle moves along the x axis with its position on the x axis at time t given by p t 2t 0 t 6 At what time is the velocity equal to 3 6 t