Question -
Answer -
(i) sin x at x = π/2
Given:
f (x) = sin x
By using the derivative formula,
[Since it is ofindeterminate form. Let us try to evaluate the limit.]
We know that 1 – cos x = 2 sin2(x/2)
(ii) x at x = 1
Given:
f (x) = x
By using the derivative formula,
(iii) 2 cos x at x = π/2
Given:
f (x) = 2 cos x
By using the derivative formula,
(iv) sin 2xat x = π/2
Solution:
Given:
f (x) = sin 2x
By using the derivative formula,
[Since it is of indeterminate form. We shall apply sandwich theorem to evaluate the limit.]
Now, multiply numerator and denominator by 2, we get