Chapter 9.1, Problem 33E

Let $f\left(x,y\right)=xy{e}^{x^2+y^2}$. Use a graphing calculator or spreadsheet to find each of the following and give a geometric interpretation of the results. (Hint: First factor $e^2$ from the limit and then evaluate the quotient at smaller and smaller values of h.)

a. $\underset{h\to 0}{\lim }\frac{f\left(1+h,1\right)-f\left(1,1\right)}{h}$

b. $\underset{h\to 0}{\lim }\frac{f\left(1,1+h\right)-f\left(1,1\right)}{h}$