Let f(x) be defined as follows r + 8r + 15 if r<-3 I+3 f(2) = < 2 -7 if r2-3 Prove from first principles (i.e.an e – 6 proof) that f is continuous at the point z = I = -3.

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A: Topic:- Functions

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Q: (a) Let x2 if x is rational f (x) = 0 otherwise. Prove that f is differentiable at 0.

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Q: Showthat fo= x| is Continuous evalyuhore- 1x1+1

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Q: (c) Suppose that f : [-1,1] →R is a continuous function such that r²+ f(x)² = 1 for every rE[-1, 1].…

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Q: 13. Let g be defined by V7x +2 V6x + 4 | g(x) = if x 2 - and x 2 x – 2 k , if x = 2 For what value…

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Q: f(x) = 3x - 5x² 1. c = 2

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