25,270 Answered Questions for the topic calculus

Calculus

06/19/23

Find the Maclaurin Polynomial of degree 7
Let F(x) = ∫ (from 0 to x) sin⁡(7^t(2)) dt.Find the MacLaurin polynomial of degree 7 for F(x).Use this polynomial to estimate the value of ∫ (from 0.62 to 0) sin⁡(7x^(2)) dx.Note: your answer to... more
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Calculus

06/18/23

Consider the parametric curve
Consider the parametric curve:x = 64−t^(2) ,y=t^(3)−16tAt which t value(s) is the tangent to this curve vertical? ( Note: If there is more than one write them as a comma separated list)t= ? Write... more
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Calculus

06/18/23

Eliminate the parameter to find the Cartesian Equation
Eliminate the parameter to find the cartesian equation of the curve: x = 2sec⁡(theta), y = 2tan⁡(theta),−(pi)/2 < (theta) < (pi)/2.The equation of the curve is: ?
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Calculus Math

06/18/23

What's the square root of -1?
How do negative numbers get broken down? We are told in school that you can't take the square root of negative numbers, but in reality it is possible.
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Calculus

06/18/23

Compute the 6th derivative of function
Compute the 6th derivative of f(x) = arctan⁡( (x^(2)) / 7)at x = 0.(f^(6)) (0) = ?
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Calculus

06/18/23

Find the degree of Taylor Polynomial
Find the degree 3 Taylor polynomial T_3(x) of function f(x) = (−3x+26)^(4/3) at a=6.T_3(x) = 
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Calculus Math

06/18/23

I was using log rules and was able to solve to the point y'=y(1/2x + 2x-1 +2/3(x+1) how did my professor simplify it to the below answer?
1/6 x -1/2 e x^2-x (x+1)-1/3 (12x3+6x2+x+3)
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Calculus

06/17/23

calculus question
Helium is being pumped into a spherical balloon at a rate of 3 cubic centimeters per second. How fast is the radius of the balloon increasing when the radius is 10 centimeters? Round your answer to... more
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Calculus

06/17/23

calculus question
At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 21 knots and ship B is sailing north at 17 knots. How fast (in knots) is the distance between the ships changing... more
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Calculus

06/17/23

calculus question
Gravel is being dumped from a conveyor belt at a rate of 50 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... more
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Calculus

06/17/23

calculus question
Helium is being pumped into a spherical balloon at a rate of 3 cubic centimeters per second. How fast is the radius of the balloon increasing when the radius is 10 centimeters? Round your answer to... more
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Calculus

06/17/23

calculus question
At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship B is sailing north at 22 knots. How fast (in knots) is the distance between the ships changing... more
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Calculus

06/17/23

Find the first 4 nonzero terms in the Series
The function f(x)=ln⁡x has a Taylor series at a=8. Find the first 4 nonzero terms in the series, that is write down the Taylor polynomial with 4 nonzero terms.
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Calculus

06/16/23

Calculus orthogonal

Find the orthogonal projection of v = 16, 12, 18, 14X1 = -3, 4, 2, -4X2 = -4, -5, 4, 0
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Calculus

06/16/23

Calculus Orthonormal
Let y = -5, -1, 3, -1V1 = 1, -4, 2, -1V2 = 2, 3, 4, -2Compute the distance d from y to the subspace of R4 spanned by V1 and V2
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Calculus

06/16/23

Calculus Orthonormal
Find an orthonormal basis of the plane x1−4x2−x3=0.
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Calculus

06/16/23

Write a partial sum for the Power Series
Consider the function ln⁡(1+8x).Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. For example, if the series were ∑n=0∞3^n x^(2n), you... more
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Calculus

06/16/23

What is Partial Sum of Power Series
Consider the function1/(1−x^3)Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. For example, if the series were ∑n=0∞3n x^2n, you... more
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Calculus

06/16/23

Find the first non-zero terms of Power Series
Find the first five non-zero terms of power series representation centered at �=0 for the function below. f(x)= x^3/(1+5x)Answer: f(x)= ?What is the interval of convergence?Answer (in interval... more
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Calculus

06/15/23

Compute the derivative of: ƒ(x) = (x^3 + 2x)e^x

e is Euler's number.Compute the derivative of:ƒ(x) = (x3 + 2x)ex Compute the integral:∫ ex(4 + ex)5 dx Compute the limit:lim x→+∞ ((e4x - e-4x)/(e4x + e-4x))
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Calculus Math

06/15/23

f(x)=x^6h(x) h(−1) = 5 h′(−1) = 8 f′(−1)=?
Given thatf(x)=x^6h(x)h(−1) = 5h′(−1) = 8f′(−1)=?
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Calculus Math

06/15/23

If , f(x) = 2x(sin x + cos x)

If , f(x) = 2x(sin x + cos x) findf′(5)
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Calculus

06/15/23

Calculus Orthonormal

Use the inner product <f,g>=∫01 f(x)g(x)dx in the vector space C0[0,1] to find the orthogonal projection of f(x)=5x^2+1 onto the subspace V spanned by g(x)=�−1/2 and ℎ(x)=1.
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Calculus

06/15/23

Calculus Orthonormal
Find the orthogonal projection ofV = 0, 0, 3, 0onto the subspace V of R4 spanned by [1, -1, -1, 1], [-1, -1, -1, -1], [-1, -1, 1,1]
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Calculus

06/15/23

Calculus Orthonormal Sets
Find the orthogonal projection of V = 16. 12, 18, 14onto the subspace V of R4 spanned byX1 = -3, 4, 2, -4X2 = -4, -5, 4, 0
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