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Show that f(x) = {(sin3x/tan2x : x < 0), (3/2 : x = 0), ((log(1 + 3x)/(e^2x - 1) : x > 0) is continuous at x = 0.

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Show that f(x) = {(sin3x/tan2x : x < 0), (3/2 : x = 0), ((log(1 + 3x)/(e2x - 1) : x > 0) is continuous at x = 0.

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1 Answer

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(iii) lim (x→0) f(x) = 3/2 = f(0)

Thus, f(x) is continuous at x = 0

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