Answer to Question #207669 in Calculus for Sarita bartwal

Question

Check the continuity of the function

f: R^2to R at(0,0) , where f is defined by

f(x,y)= e^(2x+y) + tan x

Answer 1

$$\lim\limits_{(x,y)\to(0,0)}f(x,y)=\lim\limits_{(x,y)\to(0,0)}(e^{2x+y}+\tan x)$$

$$=e^{2(0)+0}+\tan (0)=1$$

$$f(0,0)=e^{2(0)+0}+\tan (0)=1$$

Since

$$\lim\limits_{(x,y)\to(0,0)}f(x,y)=1=f(0,0),$$

then the function $f(x, y)=e^{2x+y}+\tan x$ is continuous at $(0, 0).$