1. For k € {1,..,9}, let yſk) denote the kth derivative of a function y, so y(1) = y', y(2) = y" and so on. (a) Give an

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1 For K 1 9 Let Ysk Denote The Kth Derivative Of A Function Y So Y 1 Y Y 2 Y And So On A Give An 1 (69.79 KiB) Viewed 104 times

1. For k € {1,..,9}, let yſk) denote the kth derivative of a function y, so y(1) = y', y(2) = y" and so on. (a) Give an example of a function f(x) such that lim, 40-f(x) = 2, lim, 70+ f(x) = 3, and f(0) = 1 simultaneously. (b) Give example of a linear DE for y(2) with constant coefficients, of order 2 such that one solution to this DE satisfy y(0) = 1.