7. Find the order of growth of the following sums: a) 1(i² + 1)² b) Σ=1 Σ=1(i + j)
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The order of growth of an algorithm is an approximation of the time required to run a computer program as the input size increases. The order of growth ignores the constant factor needed for fixed operations and focuses instead on the operations that increase proportional to input size.
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- b. Find the N-point Discrete Fourier Transform X[k] for the following sequence: 0sn< N- 1 x[n] = 0, %3D otherwiseQ(A). Let {fn(x)}- be a sequence of functions In=1 1+ (x – 2)“ J n=1 defined over [2,3]. Show that: (a) fn(x) is meaurable and monotonic increasing for all n. (b) {fn(x)}=1 converges a.e. to a function f(x) to be determined. 3 (c) Apply the monotone convergence theorem to evaluate Lim | fn(x)dµ. n 00Find the following sums: 1 (ii) (iii) cos(kT) k(k + 1)(k + 2) ek k=3 k=1 k=1
- 4) Let f(x)= 5 (-1)* x* (2k)! k Find [f(x)dx. Write in summation form. k = 01. Find the F.S. expansion of f(x) = x n = x < XIf En and S, is its n-th partial sum, find: 3 2. (a) lim cos(an) (b) lim S. ||Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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