Q3. Use Z-transforms to find the convolution of the following sequences: (a) 1, 0sns 10 à (n) =r. x (n) = '0, %3D otherwise
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A: As per your query the solution of question no 8 is given in the next step.
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A: The solution is below.
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Q: (6) If u, = x-Pr(x)Pn -1(x) dx, show that nu, + (n – 1)un-1 | and hence evaluate u.
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- Suppose that F(u) denotes the DFT of the sequence of f(x)={1, 2, 3, 4}? What is the value of F(14)? (Hint: DFT periodicity)(b) Give a qualitative explanation for why the sequence gn(x) = xn is not equicontinuous on [0, 1]. Is each gn uniformly continuous on [0, 1]?Find first 3 terms of the Taylor expansion of the function f(x,y) = e ^ (x+y) at the point (0,0).
- If the derivatives of a function f(x) at a=6 are f^(n)(6)=(n!/8^n)(n/n+3)^n find the Taylor series for f(x) centered at a and the radius of convergenceThe sum of a series is defined as a limit of partial sums, which means that when the ratio r satisfies −1 < r < 1, the sum of a geometric series is:How would I find if the sequences an=nπ cos(nπ) and an= (n2)(1/n) are convergent/divergent?
- Build a Taylor series approximation from scratch for f(x) = ln(x2) centered at 2 - I understand how to find the derivatives at n=1,2,3... I just don't know how to go from there; how to recognize the patterns and turn that into the sigma notationFor sequence of functions {nxe-nx} for x ∈ (0 + 1), what is the uniform norm of fn (x) - f(x) on (0 + x). is the sequence uniformly convergent?1. Consider the sequence Xn = √n + 1 − √n, n ≥ 1. Prove that (xn)n isconvergent. Find its limit.
- Suppose that ∞ n = 0 anxn converges to a function y such that y'' − 2y' + y = 0 where y(0) = 0 and y'(0) = 1. Find a formula that relates an + 2, an + 1, andIf the Taylor series forf(x) =e3x, centered atx= 0is∞∑n=03nxnn!, what is the Taylor seriesforg(x) = 3e3xcentered atx= 0?For the sequence {a_n}up ∞ down n=0 with limn→∞ a_n=0, this means the sequence diverges. T/F