Question 12 Given that the series converges where P> which of the following is true (Tn² + 1) O a. The integral. dx (x+ 1) diverges 4x dx s (7x + 1) b. (7n² + 1)' O. The integral converges od The integral ru - dx converges 5 (x+ 1)"i O e. No correct answer

Q: 0.2 1 dx to five decimal places using the power series from 1+x b) Estimate

A: Note that the power series of 11+x is: 11+x=1-x+x2-x3+x4-x5+... Replace x by x3 we have:…

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Q: 1. A) Express 0 1 4 1+x dx as a power series.

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A: We will use the power series expansion of sin(x) and then modify it to denote the given series as a…

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A: Given Power series of  Sinx at x=π2

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A: The half-range sine series of a function f(x) on an interval 0,a is given by, fx=∑n=1∞ bn sinnπxa…

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A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…

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A: we know:

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A: This is the question from Taylor's expansion with Maclaurin's form and Numerical Integration.

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A: To evaluate the limit of the given function by using power series expansion.

Q: sin?n e following series Ln = 1 n5 is convergent by using nth root test elect one: True O False

A: We will use root test to find if the given expression is convergent or not

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Q: 4. f(x)= tan-1 3.x² Cal Topic: Power Series Representation

A: The power series of the function f(x)=tan-1x is: tan-1x=x-x33+x55-x77+...   ...(1) which is…

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A: To find the values of x for which the fpllowing series converges…

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A: Given, ∑n=1∞sin1n S=sin1+(sin1)2+sin13+.... it is a geometric series where: a=sin1,  r=sin1 we know…

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