Calculus Questions

Find in terms of the constant a Limit lim h

The displacement in feet of a certain particle moving in a straight line is given by 8 t3 6 where t is measured in seconds a Find the average velocity over the given time periods 1 1 3 2 1 2 3 1 1 5 4 1 1 1 b Find the instantaneous velocity at t 1 1 2 3 4 b ft s ft s ft s ft s ft s

Evaluate the limit If the limit does not exist enter DNE Limit lim 24 7 x 16x 63 x 7

Find following limits if they exist Enter DNE if the limit does not exist 1 lim f x h x Pa 2 lim f x h x HIG 3 lim f x g x 216 4 lim rah x 5 lim ra g x g x 6 lim a f x 7 lim h x 2 1 8 lim zah x 1 zoh x g x lim f x 2 lim h x 6 lim g x 0 2 0 7 0 2 0 9 lim

Evaluate the limit Enter I for I for oo and DNE if the limit does not exist Limit lim x 4 7x 2

The point P 1 1 2 lies on the curve y x 1 x a If Q is the point x x 1 x find the slope of the secant line PQ correct to four decimal places for the following values of 1 5 2 9 4 999 3 99 5 1 5 6 1 1 7 1 01 8 1 001 1 2 3 4 5 6 7 8 LLL b Guess the slope of the tangent line to the curve at P Slope c Using the slope from part b find the equation of the tangent line to the curve at P

Evaluate the limit If the limit does not exist enter DNE Limit 0 49 lim 2 7 x 7

Fill in the table and guess the value of the limit lim f y where f y y 5y 6 y 3y 18 y 6 Y 6 002 6 001 6 0005 6 0001 f y Y 5 998 5 999 5 9995 5 9999 The limit as y 6 is f y

Use the given graph of the function f to find the following limits If a limit does not exist type DNE 1 lim f 2 2 12 2 lim f 2 3 lim f x 2 3 4 lim f a 20

Use the given graphs of the function f left in blue and g right in red to find the following limits 1 lim f x g x help limits 2 lim f x g x 3 lim f x g x 2 0 f x z 0 g x 4 lim 5 lim 24 1 3 f x 1 0 qz 3 3

Evaluate the limit If the limit does not exist enter DNE Limit lim 2 2 42 82 4

Given limx 3 g x 5 evaluate If the limit does not exist enter DNE Limit lim g x x 3

Let F be the function below If you are having a hard time seeing the picture clearly click on the picture It will expand to a larger picture on its own page so that you can inspect it more clearly Evaluate each of the following expressions Note Enter DNE if the limit does not exist or is not defined a lim F x lim F z lim F x F 1 2 1 11 b lim F x z 1 c lim F x z 3 lim F x lim F x 2 1 lim F z lim F x 2 31 F 1 F 3

Evaluate the integral 0x 81 sec 0 Ox 9 tan 0 x 9 sin 0 Ox 81 tan 0 Ox 9 sec 0 A Which trig substitution is correct for this integral O x 81 sin 0 282 1 cot 0 81 x dx B Which integral do you obtain after substituting for and simplifying Note to enter type the word theta 1134 sin de C What is the value of the above integral in terms of 0 D What is the value of the original integral in terms of x 1 1 x sin 2 sin x 1 2 4 C C

4xe dx 5x C

Match the following expressions that have the same trig values cot 180 cos 3 sin 210 tan 31 4 sin 150 cos 211 3 sin 270 tan 31 2

lim n a W i 0 1 Is n 3 4 n

f x In x 2 X

x uI X

im 0 sin x So In 1 t at dt sin x 2

2 In x 2 4 2 X X 1 dx

3 2 f x 4x 3x

im 8 CO h i 0 S 3 tc 4 n

f x In x 2 X

r 2 X x 3 3 2 X x dx 4x 4

sin In x dx

1 Solve the Initial Value Problem by using the Laplace Transform Show all your calculations y t 2y t 8y t 0 y 0 m y 0 n where m and n are last two digits of your student ID number 2 Find the Fourier Series for the periodic function f x m 1 x n x TT where m and n are last two digits of your student ID number m 4 and n 0 50 points 50 points

Which equation describes the circle with center 5 1 and radius 7 a x 5 2 y 1 7 b x 5 2 y c x 5 2 y 1 7 d x 5 2 y 1 49 1 49

The value of sin tan x cot sin sin 1 x COS cot 1 X X is equal to

98 Answer the questions below about the function whose derivative is f x 2 2 x 0 X a What are the critical points of f b On what open intervals is f increasing or decreasing c At what points if any does f assume local maximum and minimum values

Sketch the graph of a differentiable function y f x through the point 3 3 if f 3 0 and satisfies the conditions given below a f x 0 for x 3 and f x 0 for x 3 b f x 0 for x 3 and f x 0 for x 3 c f x 0 for x 3 d f x 0 for x 3 a Choose the correct graph below OA Ay OB N HINH FITT F LINT X ON C J TRITT BRIHT T TSUL HHET O 10

Answer the following questions about the function whose derivative is f x x 1 x 2 x 8 a What are the critical points of f b On what open intervals is f increasing or decreasing c At what points if any does f assume local maximum and minimum values

9 A heater of temperature 60 C is put at the middle of a straight corridor in a house It is given that the room temperature in the house without the heater is 6 C Suppose the air temperature is decreased by 2 C for every 10 cm away from the heater a What is the air temperature 2 2 m away from the heater 3 marks b Jessica thinks that 24 C is the most comfortable temperature How far should she stay from the heater 2 marks

Unit 5 Identify the inflection points and local maxima and minima of the function graphed to the right Identify the open intervals on which the function is differentiable and is concave up and concave down Question 3 of 8 Find the inflection point s Select the correct choice below and if necessary fill in the answer box to complete your choice OA The point s is are Type an ordered pair using integers or fractions Simplify your answer Use a comma to separate answers as needed OB There are no inflection points H This quiz 28 point s possible This question 4 point s possible G 2

Unit 5 Question 2 of 8 This quiz 28 point s possible This question 2 point s poss Does the function satisfy the hypotheses of the mean value theorem on the given interval Give reasons for your answer 8 9 f x x 10 11 Choose the correct answer OA No f x is differentiable for every point in 0 1 but is not continuous for every point of 0 1 B Yes f x is continuous for every point of 0 1 and differentiable for every point in 0 1 OC No f x is continuous for every point of 0 1 but is not differentiable for every point in 0 1 OD Yes f x is continuous for every point of 0 1 and differentiable for every point in 0 1

sin x 3 cos 2 S dx e 4 f In x x dx

K Find the value or values of c that satisfy the equation f c in the conclusion of the mean value theorem for the given function and interval f b f a b a kx x 3 3 10 Simplify your answer Use a comma to separate answers as needed Submit quiz CITED

x 5 S 4 2 2 dx 6 f 3 sin 2x cos 2x dx

1 fxe dx

TT 2 2x cos x dx 7

2 So 2x 1 x dx

6 sin x x dx

P I zx S G

7 fi 2x e da

3 e ln x da

xp x so x us 7 2

8 f 8x dx

6 f cos x 4x5 ln x da

e 1 5 f dx ex

4 f 10 5 dx 22