## Thomas' Calculus 13th Edition

We know if $f$ is a polynomial function and $a$ is any real number, then $\lim\limits_{x \to a}f(x)=f(a)$. Hence since $-x^2+5x-2$ is a polynomial, we have $\lim\limits_{x \to 2}(-x^2+5x-2)=-(2)^2+5(2)-2=-4+10-2=-4+8=4.$