f-x-y-e-1-r-2-1-if-r-lt-1-where-r-x-y-0-if-r-1-show-that-f-x-y-is-continuous-in-R-2-

Question Number 176652 by floor(10²Eta[1]) last updated on 24/Sep/22

f (x, y) = {\begin{cases} e^{\frac{1}{r^{2} - 1}} if r < 1, where r =∥ (x, y) ∥ \\ 0 if r ⩾ 1 \end{cases}

show that f (x, y) is continuous in R^{2}

Answered by floor(10²Eta[1]) last updated on 24/Sep/22

recall that ∥ (x, y) ∥= \sqrt{x^{2} + y^{2}}