Find the limits: lim_{(x,y)rightarrow(0,0)}cosfrac{x^2+y^3}{x+y+1}

Question
Limits and continuity
asked 2021-03-07
Find the limits:
\(\lim_{(x,y)\rightarrow(0,0)}\cos\frac{x^2+y^3}{x+y+1}\)

Answers (1)

2021-03-08
Given:
\(\lim_{(x,y)\rightarrow(0,0)}\cos\frac{x^2+y^3}{x+y+1}\)
On plugging in the value (x,y)=(0,0)
\(\lim_{(x,y)\rightarrow(0,0)}\cos\frac{x^2+y^3}{x+y+1}=\cos(\frac{0^2+0^3}{0+0+1})\)
On simplifying
\(\lim_{(x,y)\rightarrow(0,0)}\cos\frac{x^2+y^3}{x+y+1}=1\)
0

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