# Calculus

Calculus
Find a quadratic model for the sequence. -4, -4, -3, -1, 2 A.y = 0.5x^2 - 0.5x - 4 B.y = 0.5x^2 - 1.5x - 3 C.y = 4.5x^2 - 21.5x+21 D.y = -4.5x^2 + 21.4x - 21

Calculus
Find the second difference for the sequence. 7, 6, 7, 10, 15, 22, …. A.1 B.2 C.3 D.5

Pre-Calculus
Find P_(k+1) if P_(k)=2^(k-1)/k! (I used _ as a sign for a subscript) A. 2^(k+1)/(k+1)! B. 2^k/(k+1)! C. 2^(k+1)/k!+1 D. 2k/k!+1 Thank you

Calculus
If the functions f and g are defined for all real numbers and f is an antiderivative of g, which of the following statements is NOT necessarily true. (A)If g(x)>0 for all x, then f is increasing (B)If g(a)=0, then f(x) has a horizontal tangent at x=a (C)If f(x)=0 for all x...

pre calculus
can you check my work Find two different sets of parametric equations for the given rectangular equation: y=x^2+10 answer: x=t y=t^2+10 x=t^3 y=t^6+10

Calculus
(a) Compute the area of the bounded region enclosed by the curve y = e^x, the line y = 12, and the y-axis. (b) How does this area compare with the value of the integral ∫1-12(ln x dx)? Explain your answer. (A picture may be helpful.)

pre calculus
How would I graph r = cos 5Θ + n cos Θ, 0 ≤ Θ ≤ π For the integers n = -5 to n = 5. ?

Pre-Calculus
Which of the following shows the correct first step to prove the following by mathematical induction? 3 + 11 + 19 + 27 + … + (8n - 5) = n(4n - 1) A. 3 + 11 + 19 + 27 + … + (8 • 1 - 5) = 1(4 • 1 - 1) B. 8 • 1 - 5 = 1(4 • 1 - 1) C. 3 + 11 + 19 + 27 + … + (8k - 5...

Pre-Calculus
Find P + 1 if Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) (the k+1 and k in front of the P are subscripts) A. 7 + 13 + 19 + …+[6(k - 1) + 1] + (6k + 1) + [6(k + 1) + 1] B. 8 + 14 + 20 + …+[7(k - 1) + 1] + (7k + 1) C. 7 + 13 + 19 + …+(6k + 1) D. 7 + 13 + 19 + ...+[6(k...

AP Calculus AB
The fence around Wayne Manor (a rectangular plot of land) is going to be replaced. No fence will be required for the side lying along Gotham river. If the new wrought iron fence costs \$12 per meter for the side parallel to the river and \$4 per meter for the other two sides, ...

Calculus III
Hi, this question is about Langrange multipliers. Given f(x,y) = y^2 - x^2, subject to the constraint g(x,y) = 0.25x^2 + y^2 = 1, find the max and mins. So I found the partial derivatives for both f(x,y) and g(x,y): fx = -2x fy = 2y gx = 0.5x gy = 2y And set them up for the ...

Calculus
If an isosceles triangle has a fixed perimeter P, find the dimensions that maximize that area. Show how you know that it is the maximum.

calculus
The marginal cost is given by C'(x)=x^(1/3)+9. If the fixed costs are ​\$175​, find the cost of producing 8 units. thank you!!

Math (calculus) (mean values)
A company introduces a new product for which the number of units sold Ss given by the equation below, where t is the time in months. s(t) = 155(7-(9/(2+t))) a) Find he average rate of change of s(t) during the first year. I got the answer to be 1395/28 b) During what month of ...

Calculus III
Hi, this question is about Langrange multipliers. Given f(x,y) = y^2 - x^2, subject to the constraint g(x,y) = 0.25x^2 + y^2 = 1, find the max and mins. So I found the partial derivatives for both f(x,y) and g(x,y): fx = -2x fy = 2y gx = 0.5x gy = 2y And set them up for the ...

Calculus
A trough is 15 ft long and 4 ft across the top. Its ends are isosceles triangles with height 3 ft. Water runs into the trough at the rate of 2.5 ft3/min. How fast is the water level rising when it is 0.89 ft deep? Give your answer correct to 3 decimal places.

Calculus III
Hi, this question is about Langrange multipliers. Given f(x,y) = y^2 - x^2, subject to the constraint g(x,y) = 0.25x^2 + y^2 = 1, find the max and mins. So I found the partial derivatives for both f(x,y) and g(x,y): fx = -2x fy = 2y gx = 0.5x gy = 2y And set them up for the ...

Calculus
a car is traveling along a highway shaped like a parabola with its vertex at the origin. the car starts at 100 miles north and 100 miles west. there is a statue at 100 miles east and 50 miles north. at what point will the cars headlights hit the statue?

Calculus
A car moves along a straight road in such a way that its velocity (in feet per second) at any time t (in seconds) is given by v(t) = 3t * sqrt(49-t^2)

pre calculus
what is the distance between the pole and the directrix of r = 4/-2-6sintheta

Math - Calculus
Find the area of the surface of revolution generated by revolving the curve y = 3 sqrt (x), 0 <= x <= 4, about the x-axis. Okay, so I've set up the integral like this: 2pi ∫[0,4] (3 sqrt (x))(sqrt(1+(1/4x)))dx Which is coming out to 108.5, but that's not giving me the ...

calculus
A paper clip is dropped from the top of a 144‐ft tower, with an initial velocity of 16 ft/sec. Its position function is s(t) = −16t^2 + 144. What is its velocity in ft/sec when it hits the ground? –96 –64 –32 0

calculus
The position function for a particular object is s = â€“23t^2 + 65. Which of the following statements is true? The initial position is 23 The initial velocity is 0 The velocity at time t = 1 is 42 None of these

calculus
Find the local linear approximation of f(x) = e^(3x) at x = 1. y = e^3 y = e^(3(x − 1)) y = 3e^(3)(x − 1) y = 3e^(3)x − 2e^3

calculus
Rolle's theorem cannot be applied to the function f(x) = x^1/3 on the interval [–1, 1] because... f is not differentiable on the interval [–1, 1] f(–1) ≠ f(1) f is not differentiable on the interval [–1, 1] and f(–1) ≠ f(1) Rolle's theorem can be applied to f(x...

calculus
For the function f(x) = 20x^3 − 3x^5, determine the interval(s) for which f(x) increases. (–2, 2) (–∞, –2) U (2, ∞) (–2, 0) U (2, ∞) (–∞, –2) U (0, 2)

calculus
Find limit as x goes to infinity of (6x-(1/4x))/(3x-(1/x))? one half –4 negative one fourth 2

calculus
If the local linear approximation of f(x) = 2cos x + e2x at x = 2 is used to find the approximation for f(2.1), then the % error of this approximation is... greater than 15% between 11% and 15% between 5% and 10% between 0% and 4%

Calculus (vectors)
A plane must travel S15E at 720km/h. If the wind Is from S35W at 130km/h, what heading and airspeed should the pilot set to reach the destination. I got 648km/h E8.89S

calculus
Rolle's theorem cannot be applied to the function f(x) = x1/3 on the interval [–1, 1] because Answer Choices: f is not differentiable on the interval [–1, 1] f(–1) ≠ f(1) f is not differentiable on the interval [–1, 1] and f(–1) ≠ f(1) Rolle's theorem can be ...

calculus
A particle moves along the x-axis so that at time t its position is given by s(t) = (t + 3)(t −1)^3, t > 0. For what values of t is the velocity of the particle decreasing? 0 < t < 1 t > 1 t > 0 The velocity is never decreasing

pre calculus
In the rectangular coordinate system, each point (x, y) has a unique representation. Explain why this is not true for a point (r, Θ) in the polar coordinate system.

pre calculus
Explain how you sketch a plane curve given by parametric equations? What is meant by the orientation of the curve?

Calculus
Find the open intervals on which f(x) = -6x^2 + 96x + 7 is increasing or decreasing. a. increasing on (-inf, 16); decreasing on (16, inf). b. increasing on (-inf, 14); decreasing on (14, inf). c. increasing on (-inf, 84); decreasing on (84, inf). d. increasing on (-inf, 56); ...

calculus
a farmer wants to create pens along side his barn for his chicken ducks and geese. he has 600 ft of fencing and wants to create 2 equal spaces for each species. what is the largest area he could have? Also one side is along a house so no fencing is needed there. the image ...

Pre-Calculus
Can someone please explain how eccentricity can be used to classify conics.

Calculus
Use a graphing utility to graph the polar equation shown below. r = cos 5Θ + n cos Θ, 0 ≤ Θ ≤ π For the integers n = -5 to n = 5. As you graph these equations, you should see the graph change shape from a heart to a bell. I'm sorry. I'm having issues with graphing this.

Applied calculus
By using appropriate software/programming, sketch the following vector functions: 1) 2cos(2t)i + 2sin(3t)j for t within o to 2pai 2) 16sin^3ti + (13cost - 5cos2t - 2cos3t - cos4t)j for t within 0 to 2pai

Calculus
What would the smallest positive integer be for n if: y=sinx and y^(n) means the nth derivative of y with respect to x.

Calculus
If f(x)=(x^2+1)^(2-3x), then f'(1) = -3/2ln(2)-1/2 Is this correct?

Calculus
If f'(x)=-f(x) and f(1)=1, then f(x) = e^1-x Is this correct?

Calculus
If u,v, and w are nonzero differentiable functions, then the derivative of uv/w is what?

Calculus
A rectangular tank with a square​ base, an open​ top, and a volume of 4,000 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. I'm not understanding how to get started and find the optimization function (for any...

Calculus
Sinx=e^y , 0 <x <pi, what is dy/dx in terms of x?

Calculus
For what value of k will x+k/x have a relative max at x=-2

Pre Calculus
A flare is launched straight up with a velocity of 200 feet per second. The function h(t)= 200t−16t^2 models the height h(t)of the flare are at time t. How many seconds will it take for the flare to hit the ground?

Calculus
f(x)=6x^3-4x then d/dx(f(lnx)) =??

Calculus
If the line 3x-4y=0 is tangent in the first quadrant to the curve y=x^3+k, then k is? I got 1/4 is this correct?

Calculus applications
The bending moment (M) along a beam is M = WLx/2 -Wx2/2 kNm where x is the distance of a beam length L from the left hand end. W is the weight per unit length. (a) Shear force is calculated as the differential of bending moment. Find an expression for shear force and determine...

Calculus 1
In the problem, x and y are differentiable functions of t. Find dx/dt when x = 3, y = 4, and dy/dt= 2. x^2 + y2^2= 25

Calculus 1
In the problem, x and y are differentiable functions of t. Find dx/dt when x = 3, y = 4, and dy/dt= 2. x^2 + y2^2= 25

pre calculus
Find the equation of a Parabola with Vertex: (2,-1) and directrix: x= -2

Calculus 1
In the problem, x and y are differentiable functions of t. Find dx/dt when x = 3, y = 4, and dy/dt= 2. x^2 + y2^2= 25

Calculus 1
In the problem, x and y are differentiable functions of t. Find dx/dt when x = 9, y = 2, and dy/dt= 2. x^3y^2 = 2916

Calculus applications
6. The bending moment (M) along a beam is M = WLx/2 -Wx2/2 kNm where x is the distance of a beam length L from the left hand end. W is the weight per unit length. (a) Shear force is calculated as the differential of bending moment. Find an expression for shear force and ...

math
Eldon received 72 on his first calculus test. The marks were normally distributed with a mean of 60 and a standard deviation of 8. He received 80 on the next test, which was normally distributed with a mean of 75 and a standard deviation of 6. Which was the better mark, ...

pre calculus
use matrices to solve the system of equations , if possible 2x+3y+z=10 2x-3y-3z=22 4x-2y+3z=-2

Calculus
A car travelling at 50 kilometers per hour crosses a bridge over a river 10 minutes before a boat travelling at 40 kilometers per hour passes under the bridge. The river and the bridge are straight and at right angles to each other. At what rate are the car and the boat ...

Calculus
A man on a wharf is pulling in a boat by means of a rope attached to the bow of the boat 1 meter above water level and passing through a simple pulley located on the dock 8 meters above water level. If he pulls in the rope at the rate of 2 meters per second, how fast is the ...

Calculus
A stone is dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2 meters per second. How rapidly is the area enclosed by the ripple increasing at the end of 20 seconds?

Calculus
A man 1.69 meters tall is walking towards a building at the rate of 1.5 meters per second. If there is a light on the ground 15 meter from the building, how fast is the man's shadow on the building growing shorter when he is 5 meters from the building.

Calculus
A ladder 15 meters long leans against a vertical wall. If the foot of the ladder is being pulled away from the wall at the rate of 2 meters per minute. How fast is the top of the ladder sliding down the wall at the instant when the foot of the ladder is 12 meters from the wall.

pre calculus
use matrices to solve the system of equations , if possible. 2x+y+2z=4 2x+2y=5 2x-y+6z=2

Pre-calculus
Convert cartesian equation to polar form 1. x^2+y^2=4x 2. (x^2+y^2)^2=6(x^2-y^2)

calculus
if f(x) = (x-2)^(1/3) use Tylor's polynomial of degree two about c=3 to estimate the value of (1.36)^(1/3) thanks

Pre-Calculus
Given: r = 4/(-2-6sinθ) What is the distance between the pole and the directrix? A. 2 B.2/3 C.3 D.6

Calculus
Can someone help find limit using l'hopital rule lim x → ∞ ((3x-4)/(3x+2))^(3x+1), I'm trying to solve by adding ln function to both side.

Calculus
Given: r = 4/(-2-6sinθ) What is the eccentricity of the function? A. 2 B. -2 C. 3 D. -3

Calculus
Given: 5cos6Θ What is the shape of the function? A. Limacon B. Rose C. Lemniscate D. Circle

Math - Calculus
The region in the first quadrant bounded by y=6x^2 , 2x+y=8, and the y-axis is rotated about the line x=-1. The volume of the resulting solid is: Please help me set up the integral for this one, I'm not sure how to do it. I've tried ∫[-4/3,1] pi (8-2x-1)^2-(6x^2-1)^2 dx, ...

Pre-Calculus
Convert to Rectangular: r*tan theta/sec theta=2 A. y=2 B. y=1/2 C. x=2 D. x=1/2

Calculus
Convert to Polar: y/x = 4 A. r = 2 B. r = 16 C. Θ = 76 D. Undefined

Calculus
convert to polar: 2xy=3 A. r=sqrt(3sin theta cos theta) B. r=sqrt[(3sin theta cos theta)/2] C. r=[3/(2sin theta cos theta)] D.This cannot be converted without ambiguity.

Pre-Calculus
Convert to rectangular: 4=4sec theta A. y=2 B. y=4 C. x=2 D. x=4

Pre-Calculus
Convert to rectangular: theta=(2pi)/3 A. y=-sqrt3 B. y=-sqrt3x C. x=sqrt3 D. x=-sqrt3y

Calculus
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=6x^2, x=1, y=0, about the x-axis

Calculus
The region in the first quadrant bounded by y=6x^2 , 2x+y=8, and the y-axis is rotated about the line x=-1. The volume of the resulting solid is:

Calculus - Integrals
The region bounded by y=x^2, x=y^2 is rotated about the line y=-3. The volume of the resulting solid is:

Calculus
Find the volume of the solid obtained by rotating the region enclosed by the graphs of y=18-x, y=3x-6 and x=0 about the y-axis V=

Calculus
The region R is in the first quadrant and bounded by the x-axis, the y axis, and y= 3+2x-x^2. Find the volume of the solid that results when R is revolving about y+1= 0

Calculus
Find the volume of the solid generated by revolving the region in the first quadrant that is above the parabola y= 4x^2 and below the parabola y= 45-x^2 about the y-axis I just need help setting up the integral. V=∫[0,3]2pix(45-x^2)dx What am I doing wrong?

Calculus
The semicircular region bounded by the curve x=sqrt{9-y^2} and the y-axis is revolved about the line x=-3. The integral that represents its volume is V= âˆ« [a^b] f(y) dy What is f(y)? I've gotten f(y) to: (1+(sqrt(9-y^2)))^2-9 But it's not being accepted. What am I doing ...

Calculus - Integrals
Find the volume of the solid of revolution obtained by revolving region bounded by the parabolas 2y=x^2 and y^2=4x about the x-axis

Calculus
Find the volume of the solid of revolution obtained by revolving the plane region R bounded by y= x^5, the y-axis, and the line y=3 about the x-axis So far: y=x^5 is equal to x=5th root y. I've plugged that in to pi(r^2)h, and got V = pi ∫[0,3] y^(2/5) dy. so far I've gotten...

Calculus
Find the area of the region enclosed between y=4sin(x) and y=2cos(x) from x=0 to x=0.7pi. Hint: Notice that this region consists of two parts.

Calculus
Find the area of the region in the first quadrant between the curves y=x^8, and y=2x^2-x^4

deferential calculus
a woman is walking at the rate of 5 feet per second along the diameter of a circular courtyard. a light at one end of a diameter perpendicular to her path casts a shadow on the circular wall. how fast is the shadow moving along the wall when the distance from the woman to the ...

Integral Calculus
We can use this power series to approximate the constant pi: arctan(x) = (summation from n = 1 to infinity) of ((-1)^n * x^(2n+1))/(2n+1) a) First evaluate arctan(1) without the given series. (I know this is pi/4) b) Use your answer from part (a) and the power series to find a...

Calculus
A ballast is dropped from a stationary hotair balloon that is hovering at an altitude of 500 ft. The velocity of the ballast after t sec is -32t ft/sec. a) Find the height h(t) of the ballast from the ground at time t. Hint: h'(t) = -32t and h(0) = 500. h(t) = 500 - 16t^2 ft. ...

Calculus
Let F(x) = 0∫x e^(t^2)dt a) Compute limx → ∞ (xF(x))/ (e^(x^2)) b) Compute limx → 0 F(x)/(xe^(x^2))

Calculus
Let F(x) = 0∫x e^(t^2)dt a) Compute limx → ∞ (xF(x))/ (e^(x^2)) b) Compute limx → 0 F(x)/(xe^(x^2))

calculus
Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2), with x ≠ 2. Find all values of x where the graph of g has a critical value. For each critical value, state whether the graph of g has a local ...

Calculus 1
If each edge of a cube is increasing at the constant rate of 4 cm/s. How fast is the volume of the cube increasing when the length x of an edge is 11 cm long?

Calculus
Find all values of c that satisfy the Mean Value Theorem for f(x) = x^3 + 1 on [2, 4].

Pre-Calculus
Convert to rectangular: theta=2pi/3

Math -Calculus
Hi, I need help with the problem: "Use a definite integral to find the area of the region under the curve y=6-4x^2 and above the x-axis". I keep getting stuck at 6x-(4x^3/3). Thanks!!

Pre-Calculus
Which are examples of the use of parametric equations? A. Position of a person on a ferris wheel. B. Position of a ball after being thrown. C. A and B D. Neither A nor B

Pre-Calculus
Which is the best example of the use of parametric equations? A. Measuring weight on the moon. B. Finding the position of a person in a city. C. Determining the position of a satellite during a specific time of day. D. Finding the right parameters to use for a construction ...

Calculus
For which pair of functions f(x) and g(x) below will the lim(x->infinity) f(x)g(x)≠0 a)f(x) = 10x + e^-x; g(x) = (1/5x) b)f(x) = x^2; g(x) = e^-4x c)f(x) = (Lnx)^3; g(x) = 1/x d)f(x) = √x; g(x) = e^-x

Calculus
If f(x) is differentiable for the closed interval [−1, 4] such that f(−1) = −3 and f(4) = 12, then there exists a value c, −1< c < 4 such that a)f'(c)=3 b)f'(c)=0 C)f(c)=-15 d)f(c)=3 I understand that you are supposed to use the mean value theorem, but i dont ...

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