is Continuous At x = 0, Then

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Question

diffcult

Correct option is

A = – 4 & f(0) = 1

Let g(x) = sin 3x + A sin 2x + B sin x and since g(0) = h(0) = 0.

Again and exists, so

3 + 2A + B = 0 … (i)

In this case,

By similar argument,

27 + 8A + B = 0 … (ii)

So the last limit is equal to

f (0), if f is continuous at x = 0.

Solving (1) and (2), we get A = –4 and B = 5, so f(0) = 1