Chapter 13 - Section 13.1 - Finding Limits Numerically and Graphically - 13.1 Exercises - Page 905: 22

$-0.22$

Graph the function as shown, awe can see the limit exist and has a value of $-0.22$. Extra: use L'Hopital's Rule, $\lim_{x\to 0}\frac{x^2}{cos5x-cos4x}=\lim_{x\to 0}\frac{2x}{-5sin5x+4sin4x}=\lim_{x\to 0}\frac{2}{-25cos5x+16cos4x}=\frac{2}{-25+16}=-\frac{2}{9}$