Calculus Questions

The figure below shows a function f x At exactly two of the labeled points f x 0 At all of the labeled points f x 0 Select the correct signs for each of f f and f at each marked point Point f f f A A B A C E D E A

Find the linear approximation L x of f x log x at x 1 and use it to estimate log 1 15 L x log 1 15 Notice that the linear approximation of f x at x 1 is the Talor polynomial of degree 1 for f about x 1

a List the x values of all critical points of f x B Use interval notation to indicate where f x is increasing A function is increasing if larger x values give larger y values Don t include points where the function changes from increasing to decreasing or from decreasing to increasing Increasing for a in C Use interval notation to indicate where f x is decreasing A function is decreasing if larger x values give smaller y values Don t include points where the function changes from increasing to decreasing or from decreasing to increasing Decreasing for a in D List the x values of all local maxima of f x values of local maxima E List the x values of all local minima of f x values of local minima F Use interval notation to indicate where f x is concave up Concave up for a in G Use interval notation to indicate where f x is concave down Concave down for in H List the x values of all the inflection points of f values of inflection points BEB B

Given that f 2 6 1 2 and f 2 5 9 4 approximate f 2 6 f 2 6

1 point You are given the following graph of the function f 5 P 18 5 0 18 1 5 10 5 0 10 4 0 Find the x value of the point where the second derivative changes sign from negative to positive

Claire needs to borrow 12 000 from a local bank She compares the monthly payments for a 5 1 loan for three different periods of time What is the monthly payment for a one year loan A two year loan A five year loan

Evaluate the following indefinite integrals 3 1 dx 3 b 5x dx 4 4x

Evaluate the following indefinite integrals 4 cos x sin x sin x 2 csc x dx sin x a b dx

3x 3 Follow the steps for graphing a rational function to graph the function R x 5x 25 OC The function has three vertical asymptotes The leftmost asymptote is rightmost asymptote is Type equations Use integers or fractions for any numbers in the equations OD The function has no vertical asymptote the middle asymptote is and the Determine the behavior of the graph on either side of any vertical asymptotes if one exists Select the correct choice below and if necessary fill in the answer box es to complete your choice OA It approaches on one side of the asymptote s at x and o on the other It approaches either co or on both sides of the asymptote s at x Type an integer or a simplified fraction Use a comma to separate answers as needed Type each answer only once OB It approaches either or o on both sides of the asymptote s at x Type an integer or a simplified fraction Use a comma to separate answers as needed Type each answer only once OC It approaches o on one side of the asymptote s at x and o on the other Type an integer or a simplified fraction Use a comma to separate answers as needed Type each answer only once 4 OD There is no vertical asymptote

Match each of the following graphs with the correct function by placing the letter of the graph on the line provided Each letter can only be used once Do not use a calculator or desmos to draw the graph 3 f x x 1 2 2 E 4 f x x 1 F 5 f x x 2x 1 q 1 x 1 x 1 b 2 C I C 6 f x x x 1 9 1 b a X da C 3 G 7 f x x 2x 2 a a 1 b 1 CHO H 9 f x x 2x a 1 6 2 x a a 1 1 1 2 1 2 1 cia B 8 f x x 2x 9 1 f 1 0 X x 12 0 1 2 1 0 x f 1 1 2 1 1 1 X 1 0 1 0 15 1 f 1 1 1 2 1 0 1 0 1 1 x 1 1 2 1 1 f 1 1 1 1 1 olla x 1 9 1 D 2 COO D 10 f x x 2x 2 x 1 1 x 1 y 1 x 1 0 1 1 X 1 0 25 0 5 To 1 1 1 1 F 1 2 1 1 1 1 1 0 10 1 11 2 y 1 0 y 1 3 1 1

Find the quadrant in which the terminal side of 8 10 radians is located None of the other answers x One Correct Answer Four Three Three

10 973 Use the following problem to answer the questions below A man flies a kite and lets out 200 feet of string The angle of elevation of the string is 30 Make a figure and answer the following questions A To find the height off the ground the kite is you will use the trigonometric function x 50 feet Correct Answer 100 feet X cot 30 Correct Answer sin 30 B How high off the ground is the kite

Match each of the following graphs with the expect function by placing the letter of the graper on the line provided Ench letter can only be used unce Do not use a calculator os desnue to draw the graph H 1700 1 1 E 1 x x 1 4 C0 70x x Qwi 5 700 1 2 1 q 1 x 1 x 1 B a 9 1 bia Cro 51 CAD 0 2 27 CNB Cz 7 x x 2x 2 QUI cia XI X 2 1 F D 12 10 1 0 Dat 14 1 1 0 72 x 11 0 26 2 1 1 B38 x x 2x o x 1 2 1 1 1 1 9 f x x 2x 21 10 11 16 x f 1 1 2 1 1 1 0 D 10 f x x x 2 y 1 x 1 0 1 1 X 1 0 1 1 1 4 1 0 Y 1 1 4

A central angle measuring 165 is in a circle of radius 4 meters Find the length of the arc of the circle subtended by the angle Make the figure before solving the problem X Correct Answer about 660 meters about 11 5 meters about 2 9 meters about 4 meters about 11 5 meters about 4 meters

Match each of the following graphs with the correct function by placing the letter of the graph on the line provided Each letter can only be used once Do not use a calculator or desmos to draw the graph H 3 f x x 1 E 4 f x x 1 B 5 f x x 2x 1 q 1 x Q 1 b 1 C O G 6 f x x 2x 1 x 1 x 1 7 f x x 2x 2 a 1 6 2 x 2 a 3 1 1 1 2 1 2 0 8 f x x 2x o b a 2 a D 9 f x x 2x x 1 x 1 0 2 2a 2 a 1 f 1 1 1 2 1 1 1 1 27 1 0 x 2 2 x 12 10 f x x 2x 2 x 1 x 2 2 1 1 2 1 3 1 1 2 21 1 0 f 1 2 1 12 1 12 0 2 0 1 1 1

Find the range of the function f x 3 sin 3x 1 5 x Orange 8 2 Correct Answer range 8 2 range 9 2 range 8 2 range 2 8 range 2 9

71 72 The acceleration function in m s and the initial velocity are given for a particle moving along a line Find a the velocity at time t and b the distance traveled during the given time interval 71 a t t 4 v 0 5 0 t 10

5 24 Find the general indefinite integral 5 f 3x 4x 1 dx 7 f x cos x dx 9 f x 7x 5 dx 11 5 3x x dx 13 u 4 2u 1 du 6 f 5 2 x dx x 10 x dx 12 u 2u u du 14 1 31 2 dt 8 x dx I

5 24 Find the general indefinite integral 5 3x 4x 1 dx 7 f x cos x dx S f x 3 7x 25 dx 11 f 5 3x 3x dx 13 f u 4 2u 1 du 1 x x X 9 15 dx 6 f 5 2 x dx 1 x 1 8 dx I 10 x dx 12 f u 2u u du 14 t 3t 2 dt 16 x 1 x 1 ax dx x 1

Definition The collection of all antiderivatives of f is called the indefinite integral of f with respect to x and is denoted by f x dx Find the most general antiderivative by evaluating the following indefinite integral J 7 10x 12 dx NOTE The general antiderivative should contain an arbitrary constant NOTE To input for example the absolute value of timo lal or pho m

Definition The collection of all antiderivatives of f is called the indefinite integral of f with respect to x and is denoted f x da Find the most general antiderivative by evaluating the following indefinite integral 5 x 12 0 dz NOTE The general antiderivative should contain an arbitron

37 3i 5 1 39 3 21 4

A street light is at the top of a 12 ft tall pole A woman 6 ft tall walks away from the pole with a speed of 7 ft sec along a straight path How fast is the tip of her shadow moving when she is 50 ft from the base of the pole ft sec

Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute It forms a pile in the shape of a right circular cone whose base diameter and height are always equal How fast is the height of the pile increasing when the pile is 22 feet high Recall that the volume of a right circular cone with height h and radius of the base r is given by 1 V r h 3 ft min

Water is leaking out of an inverted conical tank at a rate of 12300 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate The tank has height 12 meters and the diameter at the top is 4 meters If the water level is rising at a rate of 28 centimeters per minute when the height of the water is 1 meters find the rate at which water is being pumped into the tank in cubic centimeters per minute Leave answers in 3 decimal places cm

At noon ship A is 50 nautical miles due west of ship B Ship A is sailing west at 24 knots and ship B is sailing north at 18 knots How fast in knots is the distance between the ships changing at 5 PM Note 1 knot is a speed of 1 nautical mile per hour

Next question Get a similar question You can retry this question below Given P x x 2x 25x 50 find the zeros real and non real of P The zeros are 2 51 5i Write P in factored form as a product of linear factors Be sure to write the full equation including P x 0 2 0 5i 0 5i syntax error this is not an equation

The area of a healing wound is given by A The radius is decreasing at the rate of 3 millimeter per day at the moment when r 49 How fast is the area decreasing at that moment square millimeters per day

The volume of a cylinder of height 12 inches and radius r inches is given by the formula V 12m dV Which is the correct expression for O O dV dt dV dt dV dt dV dt dV dt 24 T dt 24Tr 0 dr dt 24 r dr dh dt dt dr dt 127 dt Suppose that the radius is expanding at a rate of 0 8 inches per second How fast is the volume changing when the radius is 2 3 inches Use at least 5 decimal places in your answer second

20 Find an equation of the largest sphere with center 5 4 9 that is contained in the first octant

y 2e 2x 3x 6 y 0 5 olve the initial value problem above Do not include y in your answer

While taking a walk along the road where you live you accidentally drop your glove but you don t know where The probability density p x for having dropped the glove x kilometers from home along the road is p x 2e 2 for x 0 a What is the probability that you dropped it within 1 kilometer of home NOTE Enter the exact answer or round to three d The probability is b At what distance y from home is the probability that you dropped it within y km of home equal to 0 95 NOTE Round your answer to three decimal places y nal places km

The probability of a transistor failing between t a months and t Your answer is correct C a If the probability of failure within the first six months is 10 what is c Round your answer to four decimal places 0 0176 of c b months is given by c et dt for some constant c

Find the particular solution to the differential equation below such that y 0 7 y 5e 9x 7x Do not include y in your answer

Based on the table what is the probability that there will be a cost overrun of 50 or more Between 20 and 30 Near what percent is the cost overrun most likely to be C y 20 0 01 0 10 0 08 0 19 10 0 32 20 0 50 The most likely amount of cost overrun is 30 40 50 Enter the exact answers for the probabilities Round your answer for the most likely amount of cost overrun to the nearest percent 0 80 0 94 0 99 The probability that there will be a cost overrun of 50 or more is 50 The probability that there will be a cost overrun between 20 and 30 is 99 30

Use properties of the indefinite integral to express the following integral in terms of the simplest integrals 3x 5x dx Select the correct answer below 3 3 x dx 5 3 x dx 3x dx 5 x dx 5x dx T x dx 3 x dx 5 xdx

61 If oil leaks from a tank at a rate of r t gallons per minute at 120 time t what does 1 0 r t dt represent

Use properties of the indefinite integral to express the following integral in terms of simpler integrals 8x 2x 3 dx Select the correct answer below 08 8x dx 2 8 x dx 2 x 1 T T 8 x dx 2 2 2 0 8 x x dx 2 x 8 x dx 08 31 O 8 3 dx T 3dx T 3 dx 3 dx x dx x dx 2x dx xdx x dx x dx 2 xdx 3 dx 3 dx

Use derivatives to determine which of the functions below is the anti derivative of 2 Select the correct answer below O 2 In 2 C Ox 2 C O2 C C

57 The area of the region that lies to the right of the y axis and to the left of the parabola x 2y y the shaded region in the figure is given by the integral 2y y dy Turn your head clockwise and think of the region as lying below the curve x 2y y2 from y 0 to y 2 Find the area of the region YA 2 0 x 2y y

Evaluate the following indefinite integral 4x 3 4x6 2x5 3x 3 dx

Use properties of the indefinite integral to express the following integral in terms of simpler integrals 2x 3x 3 dx Select the correct answer below 2 3 dx x dx 3 dx 2 x dx 3 xdx 30 0 2x dx 3 02 0 2 2 dx 3x dx 3 dx 1 3 dx 0 2 x dx 3 xdx 3dx 2 x dx 3 xdx 3dx 0 2 x dx 3 x dx

Use properties of the indefinite integral to express the following integral in terms of the simplest integrals 7x Select the correct answer below 07 x dx 2x 07 1 0 7x x dx 2 2 7x dx 2 2 x0 07 x dx 2 xdx 2x dx x dx x dx 7x 2x dx

Evaluate the integral above by taking the derivative of each answer choice to determine which function is the antiderivative of 40xe5x Select the correct answer below O Ses C O4e25x C 4x5x C O4e x C

44 ST 4 3ex 0 3e 4 sec x tan x dx

Evaluate the integral above by taking the derivative of each answer choice to determine which function is the anti derivative of 5 Select the correct answer below O 5 In 5 C In s C 5 Ox 5 C 5x 1 C 5 dx O 5x 1

Using the substitution u 7 6 Re write the indefinite integral then evaluate in terms of u 7x x 6 5 dx 10 0 Note answer should be in terms of u only Part 2 Back substituting in the antiderivative you found in Part 1 above we have 15 7x x 6 5 dx

Solve the initial value problem y x 0 dy dx 1 10 y 16 0

5 24 Find the general indefinite integral 5 3x 4x 1 dx 7 f x cos x dx 6 5 2 x dx 1 8 J x 2 dx x

5 24 Find the general indefinite integral 3x 4x 1 dx 5 6 5 2 x dx