If` f(x)={(mx^2+n, x < 0),(nx+m , 0le x le1),(nx^3+m, x >1):}` .
For what integers m and n does both `lim_(x rarr 0)f(x)` and` lim_(x rarr 1)f(x)` exist?

Explanation

To determine the integers \( m \) and \( n \) for which both limits \( \lim_{x \to 0} f(x) \) and \( \lim_{x \to 1} f(x) \) exist, we need to analyze the piecewise function given:

\[
f(x) =
\begin{cases}
mx^2 + n & \text{if } x < 0 \\
nx + m & \text{if } 0 \leq x \leq 1 \\
nx^3 + m & \text{if } x > 1
...