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Prove that function f(x) = (sin pi x...

Prove that function `f(x) = (sin pi x) (x-1)^(1//5)` is continuous and differentiable at x=1
Also show that f'(x) is differentiable at x=1.

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To prove that the function \( f(x) = \sin(\pi x) (x-1)^{1/5} \) is continuous and differentiable at \( x = 1 \), and to show that \( f'(x) \) is differentiable at \( x = 1 \), we will follow these steps: ### Step 1: Check Continuity at \( x = 1 \) To check the continuity of \( f(x) \) at \( x = 1 \), we need to evaluate: 1. \( f(1) \) 2. \( \lim_{x \to 1} f(x) \) ...
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