Calculus Questions

Factor the following polynomial 4x 40x 100 4x 40x 100

Factor the polynomial 2 8x 16 8x 16

6 Select the expression that is equivalent to see cot 25 2 B S X X C 25 1 Cot 25 D E S 25

Careful here O A 1 OB 1 OC 0 OD 3 O E None of the above

ot 1 After t hours of operation an assembly line has assembled A t 20t C x 2890 70x power lawn mowers 0 st 10 Suppose that the factory s cost of manufacturing x units is C x dollars where a Express the factory s cost as a composite function of the number of hours of operation of the assembly line b What is the cost of the first 2 hours of operation a The factory s cost is BILLE

The velocity of a particle moving along a line is t 2t sin t meters per second Then the net change in position during the time interval 0 t 4 is No calculators OA 20 376 meters OB cos 16 meters O C 16 45 meters OD 21 4 meters O E 7 cos 16 meters

Which of the following are true for the vector valued function r t cos t i sin t j Select all that apply The graph of r t is a line parallel to the z axis Or t 1 for all t Olim r t j The graph of r t is a circle in the xy plane lim r t 1 0 0 1 0 r t cos t sin t 0

X 7 x Let g x g h t and h x x 4x 7 Calculate the function g h t

Let g x h g x X 2 x and h x x 4x 8 Calculate the function h g x

Let f x X X 7 and g x 12 X 12 x Express f x g x as a rational function f x g x for x Use a comma to separate answers as needed

Suppose A is a 3 x 3 matrix and B 2A Then i B 8 A ii B 4 A iii B 2 A iv B A V None of the options

The system x 0 Y Z 0 x 10 y 20 x y 2 5 x 2y 18 with the objective function p 70x 82y has a maximum of i 1028 ii 1020 iii 700 iv 732 V None of the options

Let 1 3 2 02 X 5 0 04 Then i x 0 ii x is any real number there is no value for x iv x 8 V None of the options

The point P xo yo zo is in a plane for which n a b c is a normal vector Which of the following equations must every other point Q x y z in the plane satisfy Select all that apply n PQ 0 1x PQ 0 nx ax by cz d where d axo byo czo a b c x xo y yo 2 zo 0 a x xo b y yo c zzo 0

Let x y be any two vectors in space Which of the following are properties of the cross product x Xy Select all that apply x x y is orthogonal to the plane determined by x and y x x x y 0 and y x x y 0 xxy y x x x x y is the area of the paralellogram determined by x and y xxy y x x xxx y xy 0

Suppose a 26 2 is expanded in descending powers of a Then the 5th term in the expansion is i 22 a 26 12 4 ii 12 a 26 12 1 a 26 5 iv 12 1 a 26 5 V None of the options

Suppose a ib is a complex number Then a ib is equal to i b 3ab 3a b a ii ib 3iab 3ia b a iii ib 3iab 3ia b a iv ib 3iab 3ia b a V ib 3iab 3ia b a vi None of the options

Try it Evaluate the step function for the given input vale 4 3 x 1 1 1 x 2 2 x 4 X 24 g x a Step 3 5 g 2 19 g 2 g 5

Suppose that F 12 What is the value of F given that k 9 0 x 10 Q 9 x 104 Q2 9 x 104 and r 7 x 10

If the graph of a x is horizontally compressed by one fourth to obtain the graph of b x fill in the table for b x y a x X X Y Y 4 2 1 16 12 10 After you pick your answer press GO y b x 16 12 0 8 10 4 0 8 0 8 8 8

1 point Find the Laplace transform F s L f t of the function f t est 10 h t 2 defined on the interval t 0 Here h t is the unit step function Heaviside F s L est 10h t 2 help formulas

The volume of an open topped box with a square base is 245 cubic centimeters Find the height in centimeters of the box that uses the least amount of material OA 6 centimeters OB 3 centimeters OC 7 883 centimeters OD 2 centimeters OE 3 942 centimeters

X sin 2x 2 dx OA cos 2x 3 2 C OB 3 cos 2x 3 2 C OC cos 2x 3 2 C OD cos 2x 3 2 C E None of these This one can t be done using the metho substitution

x 4x 7 Ad O A 2 42 7 C O B 2 42 7 C O C C O E 2 5 x 4x 7 5 OD None of these This one can t be done using the method substitution 4 5 x 4x 7 5 C

2s 7 7s 12 a Find the partial fraction decomposition of F s 1 point Consider the function F s 2s 7 5 7s 12 b Find the inverse Laplace transform of F s f t C F s help t

1 point Consider the initial value problem y 9y 0 y 0 3 y 0 0 a Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation Denote the Laplace transform of y t by Y s Do not move any terms from one side of the equation to the other until you get to part b below b Solve your equation for Y s Y s L y t c Take the inverse Laplace transform of both sides of the previous equation to solve for y t y t help formulas

a Find the Laplace transform F s L f t of the function f t sin wt defined on the interval t 0 F s L sin wt Hint Use a double angle trigonometric identity b For what values of s does the Laplace transform exist help inequalities help formulas

a Set up an integral for finding the Laplace transform of f t 1 6 B F s f t A where A and B help formulas b Find the antiderivative with constant term 0 corresponding to the previous part c Evaluate appropriate limits to compute the Laplace transform of f t F s L f t d Where does the Laplace transform you found exist In other words what is the domain of F s

1 point Consider the rational function A Select ALL terms below that occur in the general form of the complete partial fraction decomposition of F s The capital letters A B C L denote constants B C D E F G H Hs I s 11 A s 6 Bs C s 6 s 11 2 Es F 5 6 G s 11 Ks L F s s 11 D s 6 5 2 s 6 2 s 11

9 1 point Find the inverse Laplace transform f t L F s of the function F s 9 2 f t 1 2 5 1 5 5 2 S 5 help formulas

1 point Find the inverse Laplace transform f t L F s of the function F s 9s f 0 L 9 7 64 9s 7 s 64 help formulas

A tan x C B None of these This one can t be done using the method of substitution OC sec x C D 2 sec x C

Consider the curve given by x2 sin xy 3y2 C where Cis a constant The point 1 1 lies on this curve Use the tangent line approximation to approximate the y coordinate when x 1 01 OA 0 996 OB 1 O C 1 004 O D Cannot be determined OE 1 388 C

The position feet traveled of a car is given by the equation s t t 1 Find the time when the car is going the same speed as its average speed over the interval 0 to 10 seconds A t 2 5 B t 5 OC Never D t 0 OE t 10

sin x dx O A 4 7 5 tan x C O B 7x 2 7 5 tan x C O c 4 7 5 cotx C O D 4 7 5 cotx C OE 7x 2 7 cotx C

Jx 2 x 2 dx 3 x 4x x 2x O B x 4x C O C c x 2x C O A 1312 O D 1 3 C x 4x C x 2x C O E None of the above

function f t defined on an interval 0 t L is given Find the Fourier cosine and sine series off and sketch the graphs of the two extensions of f to which these two series converg f t sin 0 t 4

I dx 3x tan x 4 dx O A 3x 2 sec x C B 3x4 tan x 4 OB O c 6x2 tan x 4 D 6x 3 sec x C O E 3x2 tan x C

6 Below is the graph of y f x on the interval 0 8 A Based on the graph put the following in order from least to greatest xxx xxx xxx xx and f B Let A represent the average value of the function f x on the interval 061 Is there a val

5 Suppose a certain object moves in a straight line with the following velocity where is in meters per second and is in seconds v 2 1 3 sin t Without using your calculator but instead using properties of definite integrals and facts you know about area determine the net change in distance of the object from time 1 0 to time 6 seconds and find the object s average velocity on this interval

1 If r t is the rate of growth of a certain tree in feet per year where is in years what does the 40 expression r di represent

2 A population of rabbits starts off at time 0 with 225 rabbits and increases at a rate of r 1 rabbits per month where is in months 36 A What does the expression 3rd represent B What does the expression 225 r t di represent Suppose you re told that 24 425 How many rabbits are there in the population

4 Below is a graph of the function f x 5 4 3 2 1 It 4 5 6 7 y f x For what value of 0 is the average value of f x on the interval 5 c equal to 0 Exp

A particle s position in meters is given by the equation s t 5x sin 2x on the interval 1 4 minutes What is its instantaneous velocity at t 0 OA TT OB 3 O C 1 OD O E id3363061

3 The marginal cost for producing x units of a certain product is given by the formula MC 0 001x20 5x 66 5 A What is the increase in the cost of the production if the production level is raised from 200 to 400 units You may use your calculator here Hint Remember that marginal cost is the rate of change of the cost of production

A paperweight is thrown straight up with an initial upward velocity of 60 meters per second and an initial height of 6 meters The acceleration due to gravity of the object is given by a t 9 8 meters per second per second where tis in seconds The equation that describes the paperweight s velocity as a function of time tis A v t 4 9t 60 B v t 9 8t C c v t 4 9t 60 D v t 9 8t 60 E t 9 8t 60

An equation of the line tangent to the graph of f x 4x 8x 3 4 at the point where x 1is OA y 1 3 37497 x 1 B y 1 C X 1 D y 5 x 1 E y 81 384 x 1

Given that g t is continuous find the value of c if g t ct 2 cos if t 2 if t 2 32 A c 1 2 O B c 1 2 O C c 0 D c 2 E None of the above

Use your calculator to estimate sin 5 a 2241 dx you get OA 0 991 OB 0 253 OC 0 495 OD 1 236 OE 0 784

The absolute maximum value of f x x 12x on the closed interval 1 4 occurs at x OA 2 OB 0 OC 2 OD 4 E Cannot be determined