Consider the series Use the Ratio Test to show that this n2n n=1 series converges when < 1 (so when x| < 2 or -2 < x < 2). Does the power series converge at x = 2? What about at x = -2? (Note: the Ratio Test is inconclusive when x = ±2, so you will need to use another test for convergence to answer the question). M:

Q: solve y(4)-3y'''+2y''=e3x  using undetermined coefficient

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Q: The ratio test: {Pn =lan+1/anl.p3D lim Pn}. If p = 1 the series converges. n True False

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Q: n (4-x)"· / n+5 9n · 7" n=1

A: Given series is ∑n=1∞(4-x)n·n+59n·7n

Q: 8) Find a power series representation and determine the interval of convergence for 2 f(x) = 3 – x

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Q: 1.) Use the Limit Comparison Test to determine if the series converges or diverges. 1 sin().

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Use the root test to determine whether the series converges or diverges. If the test is…

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Q: If the given three vectors are coplanar, then find the value of x. A = i-2j + 3k, B = xj + 3k, C =…

A: A, B, C are coplanar.So

Q: 3. Find the interval of convergence of the given function defined by a power series. Include a check…

A: Solution is given below:

Q: 4. Let 0 ‡ b, c E Rn and define A = be E Rnxn. Show that (a) R(A) = span{b}, (b) N(A) = {x ≤ R" |…

A: (a) We are given that A = bcT                    where, c ∈ Rn     So, R(A) = { Ax : x ∈ Rn×1 }…

Q: Determine whether the following series is convergent or divergent. Explain by giving the name of the…

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