Evaluate the following limit : lim(x→π/4) (f(x) - f(π/4))/x - π/4, where f(x) = sin 2x

Question

Evaluate the following limit : \(\lim\limits_{\text x \to π/4} \cfrac{f(\text x)-f(\frac{\pi}4)}{\text x-\frac{\pi}4}, \) where f(x) = sin 2x

lim(x→π/4) (f(x) - f(π/4))/(x - π/4)

Answer 1

Given, f(x) = sin 2x

Since, \(\lim\limits_{\text x \to π/4} \cfrac{f(\text x)-f(\frac{\pi}4)}{\text x-\frac{\pi}4}\)

Hence, \(\lim\limits_{\text x \to π/4} \cfrac{f(\text x)-f(\frac{\pi}4)}{\text x-\frac{\pi}4}\) = 0