Mathematical+analysis+zorich+solutions |verified| -

Find the derivative of the function $f(x) = x^2 \sin x$.

As $x$ approaches 0, $f(g(x))$ approaches 1. mathematical+analysis+zorich+solutions

Let $f(x) = \frac1x$ and $g(x) = \frac11+x$. Find the limit of $f(g(x))$ as $x$ approaches 0. Find the derivative of the function $f(x) = x^2 \sin x$

Using the power rule of integration, we have $\int_0^1 x^2 dx = \fracx^33 \Big|_0^1 = \frac13$. mathematical+analysis+zorich+solutions

We have $f(g(x)) = f(\frac11+x) = \frac1\frac11+x = 1+x$.