Calculus Questions

6 W x 1 dx x 4x x 1 a x 1 b x 4x C z4 4x 7 Find the area under the parabola y x 1 from x 2 to x 2

7 Find the area under the parabola y x 1 from x 2 to x 2

4 Evaluate the indefinite integral 4x 3 e z 3x 7 dx a e 4x 3 C b e x 3x 7 C c 4x 3 e x 3x 7 C d e x 3x

13 If speedometer readings for a motorcycle at 20 second intervals are given in the table below then the Riemann sum t sec v t ft sec a true b false 20 40 60 17 17 20 0 23 19 23 20 19 20 20 20 is necessarily an upper estimate for the distance traveled by the cyclist in one minute 23r 1

9 A particle moves along a line so that its velocity at time t is v t measured in meters per second Find the distance traveled during the time period 0 t 2 a 1 m b 0 m c 1 m d 2 m e 3 m

a 1 m 10 Which integral or the sum of integrals represents the area betw the following two curves y 6x 2x 20x and y 2x 4x a 6x 24x dx f 6x 24x dx b 2 6x 24x dx c 2 6x 24x dx d f 6x 24x dx f 6r 24x dx e 6x 24x dx br

4 Evaluate the indefinite integral S 4x 3 e 3x 7 dx a e 4x 3 C b e x 3x 7 C c 4x 3 e x 3x 7 C d e x 3x 7

15 Find the derivative of the function g x S dz ln a b 1 c ln 24 1 d In 24 1

px 3x 14 Find the derivative of the function g x x 1 t dt a 1 x 3x b 1 t 2t 3 1 c 2 1 2 3x 3 2x 3 d 1 x 3x 2x 3

11 Find the area of the region enclosed by y 12 x and y x 6 a 36 b 70 c 18 d 72 e none of the above

a b 14 c 3 8 A particle moves along a line so that its velocity at time t is v t t 1 measured in meters per second Find the displacement of the particle during the time period 0 t 2 a 1 m b 0 m c 1 m d 2 m e 3 m

16 Evaluate sin x dx a 2 b 0 c d 1 2

3 Which substitution will you make to evaluate the indefinite integral 4x 3 sec x 3x 7 dx 4x 4 c u a u x 3x 7 b u 4x 4 c u 4x 3x d u x 3

6 Which substitution will you make to evaluate the indefinite integ x 1 dx x 4x a x 1 b x 4x c x 1 x 4x

2 Evaluate the indefinite integral f sin 5x 3 3x dx a 5 cos 5x 3 x C b cos 5x 3 x C c cos 5x 3 x C d sin 5x 3 x C e 5 cot 5x 3 x C torral

1 Evaluate the indefinite integral f cos 3x 2 dx a 3 sin 3x 2 C b sin 3x 2 C sin 3x 2 C d cos 3x 2 C e 3 tan 3x 2 C

5 Evaluate the indefinite integral f 2x sin x 1 dx a cos x 1 C b 2x cos x 1 C c cos x 1 C d none of the above

3 a Fill in the table with the exact values and their approximations where necessary 27 14 PK 2n 7n 4 S R T 37 KA 5 4 31 JT 4 2 X 1 sinx COSX b Sketch y tan x for 27 x 2 tan x m sin COSX 10 0 I 5 1 4 0 2 1 2 0 2 1 4 0 und it 2 31 TC 5 4 4 42 1 3 4 0 0 I E It 5 T L und 77 27 4 2 1 0 3 7 2n 2

A particle has a velocity modeled by v t 6 2 ln t 8 measured in cm s over the interval 1 t 6 What is the distance traveled from t 1 to t 6 You may either enter an exact answer or round your answer to the nearest tenth of a centimeter Provide your answer below

4 3 x2 Find the derivative

Suppose the rate of growth of bacteria in a Petri dish is given by q t 6 where t is given in hours and q t is given in thousands of bacteria per hour If a culture starts with 7000 bacteria find a function Q t that gives the number of bacteria in the Petri dish at any time t How many bacteria are in the dish after 4 hours You should round your answer to the nearest whole number Do not include any commas in your final answer if applicable Provide your answer below bacteria

Evaluate the indefinite integral given below 6x x 4x x x2 dx

Question Find the price demand equation for a particular brand of toothpaste at a supermarket chain when the demand is 36 tubes per week at 1 65 per tube given that the marginal price demand function p x for x number of tubes per week is given as p x 0 02e 0 04x If the supermarket chain sells 70 tubes per week what price should be set Round to the nearest cent Provide your answer below

Use substitution to evaluate the indefinite integral Provide your answer below f In 2x dx 5x In 2x 5x dx

Evaluate the indefinite integral given below e 20 Provide your answer below S e 2 csc 2x 2 csc 2x cot 2x csc 2x dx wwwww 2 csc 2x cot 2x csc 2x dx

A triangle has an area of 7 in and two of the sides of the triangle have lengths 5 in and 4 in Find the angle included by these two sides 45 573 O 0 795 44 427 no correct answer

Find a function that models the simple harmonic motion having the given properties Assume that the displacement is zero at time t amplitude 2 3 m frequency 0 5 Hz O f t 2 3 sin t O f t 2 3 sin 2t O f t 2 3 sin 2 t O f t 2 3 sin at O f t 2 3 sin 0 5 t

Graph g x x on the Cartesian plane to the right The domain of g x is The range of g x is If any of the above do not exist leave the answer box blank 654 ch 2 10 9 8 7 6 5 4 3 2 21 6 7 8 9 10

Find the terminal point P x y on the unit circle determined by t O 0 87 0 50 O 0 87 0 50 O 0 87 0 50 O 0 99 0 64 5TC 6 Round each value to the nearest hundred

Find the equivalent expression 1 sin x 1 sin x 1 sin x 1 sin x O 4 tan x sec x O 4 cot x csc x O4 tan x sec x O 4 cot x csc x O 4 cot x sec x

Use the Law of Sines to solve for all possible triangles that satisfy b 23 c 35 LB 25 conditions O ZA 119 LC 39 a 51 O ZA O ZA O ZA 117 LC 114 LC 1150 LC 40 a 55 42 a 47 40 a 49

Evaluate the indefinite integral given below Provide your answer below 20 5 dx 2e 6 x4 X5 31 dx

Use the Law of Sines to find x Let c 21 LA 58 25 24 O 46 23 A C C X 70 B

What is the side labeled x equal to if y 22 22 O 11 O 44 Y 30 X

Find the reference angle for the angle measuring O O 4 T 11 4T 15 11 4 4 T 11 15T 11

The measure of the angle 330 in standard position is given Find two positive angles and two negative angles that are coterminal with the given angle 670 1 060 70 345 690 1 050 30 390 O 710 1 020 50 360 426 786 294 654

Evaluate the definite integral below Enter an exact answer Provide your answer below S 1 3x 4x 4 dx L 3x 3 4x 4 dx

If you were to use a substitution of u sin x to evaluate the definite integral below what would the new limits of integration be Enter an exact answer Provide your answer below The new lower bound is 1 6 sin x cos x dx and the new upper bound is

20 20144338 6d168319ac2e5dbf490 c0867dd8733e6 Question 42 11 09 Watch Video Graph the function f x 3 1 on the axes below You must plot the asymptote and any two points with integer coordinates Asymptote Horizontal Show Examples

Use substitution to evaluate the definite integral given below Enter an exact answer Provide your answer below M 2 x sin 3x cos 3x dx x sin 3x cos 3x dx

Evaluate the indefinite integral given below S sin x 3 sin x sin x 4 sin x cos x dx Provide your answer below f sin x 3 sin x sin x 4 sin x cos x dx 4

1 06011 5 5 8 3 The answer above is NOT correct Find the exact length of the curve given by x 2t y 1 3 0 t 1 incorr

A mining company owns two mines These mines produce an ore that can be graded into two classes regular grade and low grade The company must produce at least 420 tons of regular grade and 540 tons of low grade ore per week The first mine produces 6 tons of regular grade and 18 tons of low grade ore per hour The second mine produces 18 tons of regular grade and 9 tons of low grade ore per hour The operating cost of the first mine is 20 000 per hour and the operating cost of the second mine is 9500 per hour The first mine can be operated no more than 37 hours a week and the second mine can be operated no more than 28 hours a week How many hours per week should each mine be operated to minimize the cost Note that the ALEKS graphing calculator can be used to make computations easier hour s Second mine hour s First mine

Find the missing side lengths Leave your answers as radicals in simplest form 25 26 30 7 3 A x 7 3 y 14 B x 14 y 7 C x 7 2 y 7 D x 7 2 y 7 3 A 60 5 3 y A x 10 y 5 B x 10 3 y 5 5 3 C x 10 3 y 3 5 3 D x 10 y 3

27 3 J 2 30 A m 3 n B m 2 5 n 3 C m n 2 3 D m 3 n 2 28 4 5 3 45 y 5 3 3 S 6 A x B x C 5 6 D x S 6 6 5 3 y 39 6 5 6 3 y y 5 y 5

Graph each function Lable all asymptotes lable any x y intercepts 4 x 2 22 f x A D 21 f x A B C 2 2 H B C D 3 x 2 The 4 M

Find the value of each trigonometric ratio 29 tan X 20 30 50 40 355554 Z 30 tan C B 12 U 35 20 37

D C 23 S x 1 A B AH 24 S x 2 1 A B 6 D 2

14 f x x 5 A S x x 3 B x x 5 C x 4x 4 D S x 1 x 15 g x 3 x A g x 5 Sx 25 2 3 B g x x 2 8 9 C g x x 4 2 D g x 2x 6 8

Divide Write your answer in fraction form 16 x 6x 10x 10x 16 x 1 11 A x 5x 5x 5 x 1 B r 5x2 5x 5 6 C r 5x2 5x 5 D x 3x 4x 6 x 1 6 x 1 6 x 1 17 4x 25x 28x 6 x 5 A 4x 5x 3 B 4x 5x 3 C 4x 5x 3 D 4x 5x 3 9 x 5 2 x 5 2 x 5 9 x 5