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Calculus

02/23/24

As the sun sets behind a 120-foot building, the building's shadow grows. How fast is the shadow growing (in feet per second) when the sun's ray make an angle of pi/3 radians?

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Calculus

02/23/24

If the telescope is 100 feet above the water level and if the boat is approaching at 10 feet per seconds, at what rate is the angle of the telescope changing when the boat is 150 feet from the shore?

A woman standing on a cliff is watching a motorboat through a telescope as the boat approaches the shoreline directly below her. If the telescope is 100 feet above the water level and if the boat... more

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Calculus

02/23/24

if the airplanes are flying at the same altitude, how fast will they be separating at 1:15 P.M.?

An airplane flying north at 640 miles per hour passes over a certain town at noon. A second airplane going east at 400 miles per hour is directly over the same town 15 minutes later. if the... more

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Calculus

02/23/24

how fast is the water level rising when the water is 4 feet deep

Water is pouring into a conical tank at the rate of 8 cubic feet per minute. If the height of the tank is 11 feet and the radius of its circular opening is 6 feet, how fast is the water level... more

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Calculus

02/23/24

how fast is the distance from the observer to the balloon increasing when the balloon is 6 feet high?

A small balloon is released at a point 150 feet away from an observer, who is on level ground. If the balloon goes straight up at a rate of 3 feet per second, how fast is the distance from the... more

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Calculus

02/23/24

Integral Calculus - surface area

The given curve is rotated about the y-axis. Find the area of the resulting surface. y=1/3x3/2, 5 ≤ x ≤ 21 It is rotated around the y axis so Ive been having trouble finding the area in terms... more

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Calculus

02/23/24

Write the first four terms of the sequence and find the limit of each sequence.

{[(-1)n+2n]/n}∞, n=1 {(-1/2)n}∞, n=2

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Calculus

02/23/24

Write the first four terms of the sequence and find the limit of each sequence.

{(1-3/n)n}∞, n=1

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Calculus

02/23/24

Write the first four terms of the sequence and find the limit of each sequence.

{(2√(n)-1)/(3+5n)}∞, n=0

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Calculus

02/23/24

Evaluate the improper integral from zero to infinity.

∫(0 to ∞)1/(x2+3x+2)dxSo I rewrote this as lim(as t approaches infinity) of ∫(0 to t)1/(x^2+3x+2)dxAnd then I used integration by parts and factored the denominator so I would get A/(x+2) +... more

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Calculus

02/23/24

Chris, who is 5 feet tall, is walking away from a street pole 20 feet high at a rate of 3 feet per second. His shadow is increasing as he walks farther away.

Chris, who is 5 feet tall, is walking away from a street pole 20 feet high at a rate of 3 feet per second. His shadow is increasing as he walks farther away.(a) Draw a picture to describe the... more

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Calculus

02/23/24

Use Wolfram Alpha (https://www.wolframalpha.com/) to sketch the curve C below

Use Wolfram Alpha (https://www.wolframalpha.com/) to sketch the curve C below. Then, draw the tangent line to the curve at \(x, y) = (2,-1) . Is the slope of this line positive or negative?(b)... more

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Calculus

02/23/24

Find the linear approximation to the function

Find the linear approximation to the function f(x) = sqrt{x^{2}-3} at x=2 . Then, use it to approximate sqrt{6} and sqrt{13} . Without doing calculator, which of the two do we expect to have... more

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Calculus

02/22/24

Volume Integral Questions

a) What definite integral can be used to determine the volume of a solid obtained by rotating the region bounded by x=2y^2, y=1, and x=0 about the y axis using the disks formula?a) What definite... more

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Calculus Math

02/22/24

A cylinder is inscribed in a right circular cone of height h and radius (at the base) equal to r. What are the dimensions of such a cylinder which has maximum volume?

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Calculus

02/22/24

Calculate 𝜑 to the nearest degree.

Let ℓ be the tangent line to the curve y = 4x2 at the point (1, 4). The angle of inclination of ℓ is the angle 𝜑 that ℓ makes with the positive direction of the x-axis. Calculate 𝜑 to the nearest... more

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Calculus

02/22/24

Let f(t) = ∛t . For a ≠ 0, find f ′(a)

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Calculus

02/22/24

Find f '(a). f(t) = (2t + 2)/ (t + 3)

Find f '(a). f(t) = (2t + 2) / (t + 3)

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Calculus

02/22/24

Find f ′(a). f(x) = 4x2 − 3x + 1

Find f ′(a).f(x) = 4x2 − 3x + 1

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Calculus

02/22/24

Are there any tutors that specialize in the software Julia specifically for calculus?

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Calculus

02/21/24

Find f ′(a). f(x) = 4x2 − 3x + 1

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Calculus

02/21/24

Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = −5 and g'(6) = 2. (Enter your answer as an equation in terms of y and x.)

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Calculus

02/21/24

Calc center of mass problem

A solid is formed by rotating the region bounded by the curve y=e−5x/2 and the x-axis between x=0 andx=1, around the x-axis. The volume of this solid is π5⋅(1−e−5). Assuming the solid has constant... more

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Calculus

02/21/24

calculus 2 work problem

A chain 68 meters long whose mass is 20 kilograms is hanging over the edge of a tall building and does not touch the ground. How much work is required to lift the top 3 meters of the chain to the... more

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Calculus Differential Equations

02/20/24

Ordinary differential equation with a model

A pond forms as water collects in a conical depression of radius a and depth h. Suppose water flows in at a constant rate k and is lost through evaporation at a rate proportional to the surface... more

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As the sun sets behind a 120-foot building, the building's shadow grows. How fast is the shadow growing (in feet per second) when the sun's ray make an angle of pi/3 radians?

If the telescope is 100 feet above the water level and if the boat is approaching at 10 feet per seconds, at what rate is the angle of the telescope changing when the boat is 150 feet from the shore?

if the airplanes are flying at the same altitude, how fast will they be separating at 1:15 P.M.?

how fast is the water level rising when the water is 4 feet deep

how fast is the distance from the observer to the balloon increasing when the balloon is 6 feet high?

Integral Calculus - surface area

Write the first four terms of the sequence and find the limit of each sequence.

Write the first four terms of the sequence and find the limit of each sequence.

Write the first four terms of the sequence and find the limit of each sequence.

Evaluate the improper integral from zero to infinity.

Chris, who is 5 feet tall, is walking away from a street pole 20 feet high at a rate of 3 feet per second. His shadow is increasing as he walks farther away.

Use Wolfram Alpha (https://www.wolframalpha.com/) to sketch the curve C below

Find the linear approximation to the function

Volume Integral Questions

A cylinder is inscribed in a right circular cone of height h and radius (at the base) equal to r. What are the dimensions of such a cylinder which has maximum volume?

Calculate 𝜑 to the nearest degree.

Let f(t) = ∛t . For a ≠ 0, find f ′(a)

Find f '(a). f(t) = (2t + 2)/ (t + 3)

Find f ′(a). f(x) = 4x2 − 3x + 1

Are there any tutors that specialize in the software Julia specifically for calculus?

Find f ′(a). f(x) = 4x2 − 3x + 1

Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = −5 and g'(6) = 2. (Enter your answer as an equation in terms of y and x.)

Calc center of mass problem

calculus 2 work problem

Ordinary differential equation with a model

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