1.

If f(x) = (sin x/x) when x ≠ 0, f(0) = 1, f(x), x = 0 is f(x) continuous at x = 0, why ?

Answer»

f(x) = sin x/x

Given the function f(x) = (sin x/x) : x = 0

limh → 0- f(x) = limh → 0+ f(x) = f(0)

Now, limh → 0- f(x) = limh → 0- (sin x/x)

limh → 0- (sin(x - h))/(x - h)) = 1

And, limh → 0+ f(x) = limh → 0+ (sin x/x) = limh → 0 (sin (x + h)/(x + h)) = 1

Hence, limh → 0- f(x) = limh → 0+ f(x) = f(0) = 1 



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