Mathematics - Limits Question with Solution | TestHub

Given $f(x)=\sin x,g(x)=\cos x,h(x)=x^2$ ${\lim }_{x\to 1}\frac{f(g(h(x)))-f(g(h(1)))}{x-1}$ When limit it applied, it gives $\frac{0}{0}$ form, so we apply L'Hospital rule. $\Rightarrow {\lim }_{x\to 1}\frac{\cos \left(\cos x^2\right)\left(-\sin x^2\right)(2x)-0}{1-0}$ Apply the limit, $\Rightarrow -2(1)\sin (1)\cos (\cos 1)$ $=-2\sin (1)\cos (\cos 1)$