25,270 Answered Questions for the topic calculus

Calculus

04/02/24

Need help with a power series representation and radius of convergence question.
Using differentiation or integrals, find a power series representation for the function and determine the radius of convergence.x2tan-1(x3)
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Calculus

04/02/24

Use the power series for tan^-1(x) to prove the following series for pi as the sum of an infinite series
π = 2√(3)∑(n=0 to ∞)(-1)n/[(2n+1)(3n)]
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Calculus

04/02/24

Use the power series to approximate the definite integral to six decimal places.
(0 to 0.3)∫ (x2)/(1+x4)dx
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Calculus

04/02/24

I need help with finding a power series representation for the function and determining the radius of convergence.
f(x)=(x/(2-x))3I'm not sure what the first step would be. Would I first just consider the function as 1/(2-x) and find series notation?
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Calculus

04/02/24

Using differentiation or integrals, find a power series representation for the function and determine the radius of convergence.
f(x)=x2tan-2(x3)I first found the derivative of the function, which led me to 2xtan-1(x3)+x2[(3x2)/(1+x6)]... I'm not sure if I'm wording this question right, but how do you know whether to find... more
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Calculus

04/02/24

Need help for a power series representation question.
f(x)=x/(2x2+1)I was told to consider 1/(2x2+1) first, and I got ∑(2x2)n for that... but I'm not sure what to do after that point. If we're writing this as a geometric series, then would x in the... more
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Calculus

04/02/24

Find f prime of a

Find f’a f(t) = 1/t^2+1
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Calculus

04/01/24

Find the absolute minimum and absolute maximum values of f on the given interval.
f(t) = t36 − t^2,    [−1, 6]
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Calculus

04/01/24

Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = x/x^2 + 1,    [0, 4]
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Calculus

04/01/24

Sketch the graph of f by hand and use your sketch to find the absolute maximum and minimum values of f. (If an answer does not exist, enter DNE.)
f(x) =  3 − x      if 0 ≤ x < 4 4x − 16 if 4 ≤ x ≤ 9
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Calculus

04/01/24

Sketch the graph of f by hand and use your sketch to find the absolute maximum and minimum values of f. (If an answer does not exist, enter DNE.)
f(x) =  36 − x2    if −6 ≤ x < 0 2x − 1 if 0 ≤ x ≤ 6
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Calculus

04/01/24

Let f(x) = −x^4 − 2x^3 + 6x + 5.
a) Find the interval(s) where f(x) is concave up. (Enter your answer using interval notation.) (b)Find the interval(s) where f(x) is concave down. (Enter your answer using interval... more
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Calculus

04/01/24

The function f(x) has a domain of (−∞, −1) ∪ (−1, ∞) and a second derivative given by the following.
f ''(x) = −2(x + 5)^11(x − 6)^7(x + 1)/(x + 1)Find the x-value(s) of the inflection points of f(x). (Enter your answers as a comma-separated list. If there are no inflection points, enter NONE.)
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Calculus

04/01/24

Find f ''(x) for f(x) = x^3 − 4x^2 − 3.
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Calculus

04/01/24

Suppose that f(x) = (x + 1)(x − 1)^2.
a)Find all critical values of f(x). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) (b)Find the x-coordinates of all local maxima of f(x). (Enter your... more
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Calculus

04/01/24

Let f(x) = x^2 − 9x − 52.
a) Find the interval(s) where f(x)  is increasing. (Enter your answer using interval notation.)b) Find the interval(s) where f(x) is decreasing. (Enter your answer using interval notation.)c)Find... more
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Calculus

03/31/24

Related Rates: Clock
Please answer with work too. The hour hand of a clock is 5 inches long and the minute hand is 7 inches long. At the moment the hour hand is positioned at 4 and the minute hand is positioned at 5,... more
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03/31/24

Which of the following statements is true? (calculus)
Consider the series from n=1 to ∞ ∑an , where an = ((e^(n-1))(√n+6))/(n+6)!In this problem you must attempt to use the Ratio Test to decide whether the series converges.Compute L=lim as n... more
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03/31/24

Check all of the following that are true for the series

Check all of the following that are true for the series from n=1 to ∞ ∑ (5-cosn)/n.A. This series convergesB. This series divergesC. The integral test can be used to determine convergence of this... more
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Calculus

03/31/24

Calculus Optimization Problem
An energy drink container in the shape of a right circular cylinder must have a volume of 11 fluid ounces (1 fluid ounce is approximately 1.80469 cubic inches). The cost per square inch of... more
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Calculus Math

03/31/24

please help thank u
find the derivative of the function f(x)= sin^-1 [(3x^5 -4)^3]
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Calculus Math

03/31/24

please help!!!!
find y'' by implicit differentiation; √x + √y = 1
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Calculus Math

03/31/24

please help!!!!
find the derivative of the function g(x)= 8^2x^2cos(4-5x^3) the cos(4-5x^3) is on the same level as the 2x. it is not being multiplied by 8^2x^2 its apart of it
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Calculus Math

03/31/24

Please help thank u

Find dx /dy implicit differentiation: y^2sinx+x^3cos y = sin x cos y
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Calculus

03/31/24

Find the equations of any horizontal asymptotes: 4|x|/x+4
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