Question

Let f(x)=sinx,x=0 and Δx be a small change in x. Find a first approximation to sin(Δx). Use this to say whether sin(Δx)≈Δx is true or false.

Answer 1

Since $\lim\limits_{\Delta x\to 0}\frac{\sin\Delta x}{\Delta x}=1$, we obtain that $\Delta x$ is a first approximation of $\sin\Delta x$. Then $\sin\Delta x\approx\Delta x$ is true.