Answer to Question #207669 in Calculus for Sarita bartwal

Question #207669

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


1
Expert's answer
2021-06-18T09:24:12-0400
lim(x,y)(0,0)f(x,y)=lim(x,y)(0,0)(e2x+y+tanx)\lim\limits_{(x,y)\to(0,0)}f(x,y)=\lim\limits_{(x,y)\to(0,0)}(e^{2x+y}+\tan x)

=e2(0)+0+tan(0)=1=e^{2(0)+0}+\tan (0)=1

f(0,0)=e2(0)+0+tan(0)=1f(0,0)=e^{2(0)+0}+\tan (0)=1

Since


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

then the function f(x,y)=e2x+y+tanxf(x, y)=e^{2x+y}+\tan x is continuous at (0,0).(0, 0).



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