I need to apply the divergence test to the series. However, I am stuck, how do you take the derivative of ln^10(x)

Q: What is the coefficient of x4 in the MacLaurin series for f(x) = e^(-x/2)?

A: Here we will find out the required value.

Q: Find the Maclaurin series for f(x) = e^(5x) , at a=0

A: The solution is given as

Q: Using the fact that e^x=∞∑n=0 x^n/n^! can you find a series for the function e^x^2?

A: Given: ex=∑n=0∞xnn!   ...(1)

Q: PROBLEM 3, (I +az²)y" +bzy' tay=0 in the Formof a Power Series inx.

A: By using power series  method

Q: What is the power series representation of (1-cos(x^2))/x^2?

A:

Q: Given f(x)=x/(x^2+4) find f''(x). Please do on paper.

A:

Q: Use the formula to find the first five terms of the Maclaurin’s series for   e^(2x) find the value…

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Q: Determine if  ∫3-2(1/x^3)dx  is convergent or divergent.

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Q: xy'=y+x     expand on x =1   (power series)

A:

Q: To approximate the profit from the production and sale of the 145th skirt, what value do you plug…

A: P(x) denotes the profit function and P'(x) denotes the marginal profit function.

Q: Find the first three terms of the Maclaurin series of f (x) and use it to calculate f ^(3)(0).

A: Given: f(x)=x2-xex2 A Maclaurin series is given by fx=∑n=0∞fnan!xn Here n=3, therefore we get…

Q: (a) Show that e /yu dy exists, by considering the series (e/n)". (b) Show that 1 (log n)los n…

A: Given : ∑n=2∞logn-k  and ∑n=2∞logn-n two series where 1st diverges and 2nd converges.  Integral test…

Q: find the integral of sin(x^2) by using the mclauren series of sin(x)

A:

Q: The function defined by ?(?)=3x^2−5x−2 changes sign in the interval [1, 3]. Use seven iterations of…

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Q: tan"x dxwith an error of magnitude no greater Use the series to estimate the integral than 10

A: The Maclaurin series for tan-1x is given by the formula: tan-1x=∑n=0∞-1nx2n+12n+1 Hence, the given…

Q: 9 – cosh a f(x) = 9 + cosh a

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Q: I= = *0.5 I = 5x¹e-x² dx (lerror| < 0.001)

A:

Q: A small company of science writers found that its rate of profit (in thousands of dollars) after t…

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Q: sin x – e-* = 0, [0,1]

A: We need to find the solution of the given function fixed-point iteration. Consider,  f(x)=sinx-e-x=0…

Q: Obtain the power series solution of the following ODE near x = 0. 2xy^"+(1-2x^2)y^' -4xy=0

A: Sol:- We can start by assuming a power series solution of the form: y(x) = a0 + a1 x + a2 x2 + a3 x3…