Calculus Questions

1 f x sin x e dx

2 f 2x cos 3x ln x dx

c 92 S S s sino sin 0 5 cos do

u b c f 2X Fs dx

The function f is given by f x 5 0 7 Which of the following describes f B The function f models exponential decay and lim f x 0 The function f models exponential decay and lim f x 8 The function f models exponential growth and lim f x 0 z 00 The function f models exponential growth and lim f x Z 80

u b S sto 5 x 2X fxsts T c S 5 sine XP XP 5 cus de

Product Rule f x g x f x g x g x f x dx Quotient Rule f x dx g x No 1 Find a f x b cus x F x g x f x f x g x g x the derivative 5 Sins cus S y 5 In cos sx 5 C

a trung integral berikut 4 b 2 sx s x 2 te 3 dx dx 5 sme scuso do

The functions f and g are given by f x and g x What is the domain of the function h given by h x f g x A B All real numbers All real numbers not equal to 0 All real numbers greater than 0 All real numbers greater than or equal to 0

The function f is given by x x 1 and the function g is given by g x 2 3 Which of the following is an expression for f g x I B D 2 37 2 3 7 2 6x49 1 1

4 The function k is given by k x 92 Which of the following expressions also defines k x B O 2 31 3 2x 3 32 3 2

8 Using vectors explain how to determine the volume of the following parallelepiped Determine its volume B 6 3 5 A 4 0 0 O C 2 3 5 y D 6 5 3

1 Find a f x b cus x F x the derivative 5 Sins cus 5 y 5 In Los 5x 5 sesx 5x 1

5 A father is pulling his son on a sled at an angle of 20 with the horizontal with a force of 25 lb He pulls the sled in a straight path of 50 ft How much work was done by the man pulling the sled to the nearest unit 20 25 lb

11 The scalar projection of a onto b is 8 If the length of a is 11 then what is the angle to the nearest degree between a and b

The function fis defined by f x 4 for 2 x 0 Which of the following expressions defines f x B 4 for 2 x 0 4 2 for 2 x 0 4 for 0 x 2 4 2 for 0 x 2

Two functions f and g are composed such that f g x 4 x 3 2 Which of the following could be the expressions for f x and g x A B f x x and g x 4x 3 f x 4x 3 and g x f x x 3 and g x 4x 2 f x 4x 2 and g x x 3

The function mis given by m x 36 2 2 Which of the following expressions could also define m x Jhry B 62 6 62 18 18 362

A water tank is leaking water from a crack in its base The amount of water in hundreds of gallons remaining in the tank t hours after the crack formed can be modeled by W a decreasi function of time t Which of the following gives a verbal representation of the function W1 the inverse function of W A W is an increasing function of the amount of time after the crack formed W is a decreasing function of the amount of time after the crack formed W is an increasing function of the amount of water in the tank 1 W is a decreasing function of the amount of water in the tank

Which of the following includes the input output pairs 2 4 and 3 8 A B D The arithmetic sequence an 4n The linear function f n 2 4 n 1 The geometric sequence gn 2 n 1 The exponential function h n 2 2 1

The function h is given by h x 5 3 1 2 What is the value of h 1 A B 5 3 15 5 9 4283

The function fis given by f x 9 25 Which of the following is an equivalent form for f x B f x 3 5 2 f x 3 5 22 f x 9 5 2 2 f x 9 5 21

d y dy 2y t 2 dt 2 dt

The function f is given by f x 27 and the function g is given by g x f For which of the following transformations is the graph of g the image of the graph of f A B D A horizontal translation to the left 3 units A horizontal translation to the right 3 units A vertical translation up unit A vertical translation down unit

The functions f and g are given by f x 2 and g x 2 2 where a 0 Which of the following describes the relationship between the graph of f and the graph of g A B C D The graph of g is a vertical translation of the graph of f by a units The graph of g is a horizontal translation of the graph of f by a units The graph of g is a vertical translation of the graph of f by a units The graph of g is a horizontal translation of the graph of f by a units E

An exponential function G has a known common ratio of and includes the input ouut pair 1 4 Which of the following could define G z B C 4 1 x 1 4 4

Where did they do it Hint Find the position at each time to the right t 0 On a playground t 1 5 At a baseball game The position of a vehicle moving in a straight line is Then s t t 3t 6 At which time is the particle determine moving towards the origin Why did they do it t 2 At Tony Stark s house velocity t 3 In a library The velocity of a particle is v t t 11t 2 Is the particle speeding up or slowing down at t 3 Slowing down bc a 3 0 Hates his costume Slowing down bc v 3 0 They are a Superman fan Speeding up bc a 3 v 3 0 They think spiders are creepy Speeding up bc a 3 0 Spiderman made fun of them

3 The area of a parallelogram is 104 m and the lengths of its sides are 9 m and 13 m Determine the measure of the acute interior angle of the parallelogram Round to the nearest degree

lim x40 e5x 1 3x

A 0 6 2 0 1 3 0 A B a Find A21 b Simplify and find 2AAT 5ABT 3ABT 2 Solve these systems 2x1 2x2 4x3 6 2x13x2 x3 19 3x2 4x3 13 3x1x24x3 1 3 Find production level which satisfies this consumption matrix and demand vec 2x1 x2 2x3 8 21 3x3 1 3x12x2 11 0 1 0 25 0 25 0 3 0 5 2 0 0 3 0 2 0 25 50 3 6 1 0 B X1 S 10 20 30

1 Find limits a 1 point b 1 point c 1 point d 1 point x 4 lim 22 2x 2x 12 lim 2 1 3 Find derivatives a 1 point using definition y x 5 b 1 point cos 2ry 5x 3y c 1 point y x inz 4 1 5 point You have a function x2 4x 20 5 e 2 1 lim 2 0 3r lim e x PIX 2 1 5 point What type of breakpoint function h r has in point 3 h x 23 if x 3 if r 3 f x 2 1 x 3 Find critical points of the function check which of them are minimum and which of them are maxim Find the intervals in which function is increasing and in which it is decreasing

1 If A7x5 is a coefficient matrix how many unknown variables system of linear equation has 5 2 When it is possible to say that det A is equal 0 without any calculation If three rows are equal If all elements in one column are equal to 0 If we have diagonal matrix 3 What are the properties for bounden function f x f x A f x B bounded function always has limit not all bounded functions have limit when z 7 12 35 4 If lim f x 3 and lim 1 1 removable breakpoint first type breakpoint 6 second type breakpoint function is continuous at point ro f x what type of breakpoint to is 5 Which point s are critical points Points where function is equal zero or does not exists Points where function s derivative is equal zero or does not exists Points where function s second order derivative is equal zero or does not exists Extreme points Inflection points

megd Name Pd2 Date 12 19 3 Your student email account requires you to choose a password of 4 letters followed by 1 Hour

1 The table shows the total weight of shrimp a fisherman catches each week Time weeks Weight pounds 2 3 5 6 110 130 170 500 530 What is the average rate of change from Week 2 to 5 in pounds per week

Problem 3 1 point Find a simplified expression for sin 2x 1 cos 2x A tan r B cotx C sec x D CSC C E 1

Problem 1 1 point On which interval is f x 1 e6r decreasing A 0 B C 3 1 D 0 0 E 1 2 00

Problem 5 1 point If f x ln lnx find f e D In 2 E 1 2 B C 2 10 1 A 27 Problem 6 1 point Find the area of the region enclosed by the curves y 360x a y 10x A 6426 B 6480 C 6462 D 6372 E 6444

Problem 9 1 point Suppose the line y 8 r 1 is tangent to the curve y f x at x 5 If Newton s method is used for the approximation of a solution to f x 0 and the initial approximation is 5 find the second approximation 22 A 1 B 8 C 1 8 D 1 E 0 Problem 10 1 point Find the equation of the tangent line at defined by the equation y x x 1 0 B y 2 2 A Y E y 1 1 21 01 1 1 2 4 720 1 2 4 2 C y 2 2 1 2 2 1 X 2 2 to the curve D y 2 1

Problem 31 1 point Compute the integral f 2 sin x cos x dx A 3 5 B C D 4E 2 24 7 15 Problem 32 1 point Compute the integral f 3 cos x cos 5x dx 3 A 2 B 2 C 3 D 2 2 E V3 16 20 12

Problem 30 1 point If f t 7 1 sin t 6 cos t and f 0 5 find f A 128 D 131 C 130 B 129 E 132

Problem 29 1 point Which of the below areas are equal to the following limit 2 lim n i 1 3 2 3i n i The area under the graph of 2 x from x 0 to x 3 ii The area under the graph of from x 2 to x 5 iii The area under the graph of 1 x from x 0 to x 3 A only i B only ii C only i and ii D only iii E only ii and iii C F

Problem 8 1 point If the tangent line to y f x at 2 1 passes through the point 1 1 find f 2 and f 2 A 2 and 1 B 2 and 1 C 1 and 1 D 2 and 0 E 1 and 0

Problem 4 1 point Let f x sin x2 Which of the following statements is true A f is invertible on 7 0 1 1 D f is invertible on 0 B f is invertible on 2 0 C f is invertible on E f is invertible on 0 2

Problem A 22 2 5 1 point If f x ln lnx find f e B 12 C 2 1 D In 2 E 1 2 e

Problem 2 1 point Evaluate the following limit 2x A 3 3 B 3 12 C D 4 lim 0 cos 3x 1 E 1 3

f t dt 8 3 f t dt sf t 3 dt f f t 33d 1381 3 3 4 2 26 f t dt dt 4

Find two positive numbers whose product is 143 and whose sum is a minimum

Find the indicated limit lim x In x3400 x 0 lim x Inx int 3400

Find f x and find the value s of x where the tangent line is horizontal f x x 14x 63 f x X 7 7 2 x 14x 63 Select the correct choice below and fill in any answer boxes in your choice O A The value s of x where the tangent line is horizontal is Use a comma to separate answers as needed OB The tangent line is never horizontal

For the function below find A f x B the partition numbers for f C the critical numbers of f 7 X 4 f x A X B Find the partition numbers for f Select the correct choice below and if necessary fill in the answer box to complete your choic OA The partition number s is are x OB There are no partition numbers C Find the critical numbers of f Select the correct choice below and if necessary fill in the answer box to complete your choice OA The critical number s is are x OB There are no critical numbers Use a comma to separate answers as needed Use a comma to separate answers as needed