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

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

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
$$\lim_{(x,y)\rightarrow(0,0)}\cos\frac{x^2+y^3}{x+y+1}=1$$

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