Calculus Solutions Ex#1.6

  Q.01 Find the discontinuities if any Solution: $\quad f(x)=\sin \left(x^{2}-2\right)$ This a composition of two functions. Let $$g(x)=x^{2}-2$$ and $$h(x)=\sin x$$ so we can write $$f(x)=h(g(x))$$ $g(x)$ is a polynomial which is continuous everywhere, and $h(x)=\sin x$ is continuous on $(-\infty,+\infty)$. Therefore, their composition is continuous ie $f(x)$ is continuous everywhere. There is no … Read more