Discuss the continuity of the function and evaluate the limit of f(x, y) (if it exists) as (x, y)\rightarrow (0, 0). f(x, y) = 1 - \frac{\cos(x^{2}+y^

ka1leE

ka1leE

Answered question

2021-06-13

Discuss the continuity of the function and evaluate the limit of f(x, y) (if it exists) as (x,y)(0,0).f(x,y)=1cos(x2+y2)x2+y2

Answer & Explanation

Clara Reese

Clara Reese

Skilled2021-06-14Added 120 answers

The function is continuous everywhere except the origin (0,0) - since the cosine function is continuous everywhere and the denominator is 0 only at the origin.
the limit does not exist - one can consider z=x2+y2, when (x,y)(0,0),z0+, and cos(z)1, but the denominator goes to , thus the limit does not exist.

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