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in Continuity and Differentiability by (31.3k points)
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Find a and b if f is continuous at x = 1, where

\(f(x) = \frac{sin\,\pi x}{(x - 1)} + a,\) x < 1

f(x) = (sin πx)/(x - 1) + a, x < 1

= 2π, x = 1

\(=\frac{1 + cos\,\pi x}{\pi(1 - x)^2} + b, x > 1\)

1 Answer

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Best answer

f(x) = (sin πx)/(x - 1) + a

Given, f is continuous at x = 1 and f (1) = 2π

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