25,270 Answered Questions for the topic calculus

06/03/24

A polynomial function is given. U(x) = −x3 + 3x2. Y→_______ as x→ ∞
3.2 Polynomial functions (a)
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Calculus

06/03/24

Solve the following word problem using integrals.

A water storage tank has the shape of a cylinder with diameter 10 feet. It is mounted so that the circular cross-sections are vertical. If the depth of the water is 8 feet, what percentage of the... more
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Calculus

06/01/24

Calculus: Limits
What makes a limit become non existence?I know that on a graph, you can tell if a limit exists or not when a^- and a^+ are equal. But if I am finding the limit algebraically or by using a table,... more
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Calculus

06/01/24

Find the intervals on which f(x) = sec(x)csc(x), 0 <= x <= 2pi, is increasing.
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Calculus

05/31/24

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. x = 4y^2, y ≥ 0,   x = 4;   about y = 2
I tried solving this question by simplifying: integrate (from 0 to 4) 2pi (2- (√x /2))• x dx and I got 96pi / 5 but the professor marked it wrong so I wanted to see what is the right way to solve... more
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Calculus

05/31/24

Find two unit vectors orthogonal to both given vectors. <3, −3, 3> , <0, 6, 6>
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Calculus

05/30/24

Inflection Points on Polar Curve
For what values of Α > 0 has the polar curve r(θ) = Α +cos(θ) inflection points?
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05/30/24

Find the slope of the line through P and Q. P(6, −3), Q(3, −3)
1.10 Lines (5)
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05/30/24

Find the slope of the line through P and Q. P(−8, 1), Q(5, −4)
1.10 Lines
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Calculus Precalculus

05/30/24

Find an equation of the line that satisfies the given conditions. Through (−3, 5); slope −1
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Calculus Precalculus

05/30/24

Find an equation of the line that satisfies the given conditions. Slope 2; y-intercept −3
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Calculus

05/29/24

Ropes 3 m and 5 m in length are fastened to a holiday decoration that is suspended over a town square.
Ropes 3 m and 5 m in length are fastened to a holiday decoration that is suspended over a town square. The decoration has a weight of 9 kg. The ropes, fastened at different heights, make angles of... more
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Calculus

05/29/24

Find the angle between the vectors. (Round your answer to the nearest degree.) a = ‹-8, 6› b = ‹√11, 5›
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Calculus

05/29/24

Finding area between two curves

Find the area between the two curves. Sketch both to figure out the bounds of integration with respect to x.f(x)=-x2+10, g(x)=x2+2.
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Calculus Math

05/29/24

CALC BC Lemniscate area bounded by curve
The graph of the lemniscate 𝑟=𝑘𝑐𝑜𝑠2𝜃 where 𝑘 is a constant is shown in the figure to the right. Find the area bounded by the curve.(A) 𝑘^2/4(B) 𝑘^2/2(C) 𝑘^2(D) 2
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Calculus Math

05/29/24

Calculus BC instantaneous rate of change
Point 𝑃(𝑥,𝑦) moves in the 𝑥𝑦-plane in such a way that 𝑥=1(2𝑡+1)2 and 𝑦=𝑡𝑙𝑛𝑡 for 𝑡>0. Find the instantaneous rate of change of 𝑦 with respect... more
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Calculus

05/28/24

Evaluate the limit. limit as x approaches 1 of (x^1/5 - 1)/(x-1)
Evaluate the following limit: Limit as x approaches 1 of (x1/5-1)/(x-1).
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Calculus

05/28/24

Force, stretching, and natural length???
A force of 3 pounds is required to hold a spring stretched 0.5 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.7 feet... more
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Calculus

05/28/24

Finding Volume of the solid
Find the volume of the solid obtained by rotating the region bounded by 𝑦=𝑥^2 , 𝑦=0, and 𝑥=3, about the 𝑦-axis.𝑉= Please show work! :D
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Calculus

05/28/24

Regions enclosed by curves
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.𝑦=4𝑥^2, 𝑦=𝑥^2+2Please show work! :D
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Calculus

05/28/24

Regions enclosed by curves
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.𝑦=4𝑥^2, 𝑦=𝑥^2+2Please show work! :D
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05/25/24

Finding limit of a given function
How do I find the limit, if it exists, and how do I sketch its graph:. 2-x, x≤0lim f(x), where f(x) = {x→0 . x+2, x>0
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Calculus

05/24/24

With the domain of (-pi/4<=pi/4), how is ln|secx+tanx|=ln|3+2sqrt(2)| ?
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Calculus

05/24/24

Leaving a review
Hello,I am wanting to leave a good review for a tutor my son had but I am not able to find where/how to do that. Please advise ,thank you,Kelly
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Calculus

05/22/24

What dimensions will result in the rectangular portion of the window having the largest possible area
A norman window is in the shape of a semi-circle atop a rectangle, as shown. The distance around the outside of the window is 40 feet. What dimensions will result in the rectangular portion of the... more
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