limit t

show that -------
Lt (2+x)sin(2+x) - 2sin2 x = 2cos2 + 2sin2
x→ 0

3 Answers

481
Anurag Ghosh ·

I think the RHS should be 2cos2 + sin2

535
Aditya Agarwal ·

the function given is f(x)= x.sin(x).

So we can find the limit of this function by simple differentiation.
(It will be continuous at x=2 since it is a composition of 2 continuous functions)

f'(x) = xcosx + sinx
f'(2) = 2cos2 + sin2

481
Anurag Ghosh ·

Or simply apply L'Hospital

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