Question

find limit of ysin(1/(x^4+y^4)) as (x,y)--->(0,0)

Answer 1

It would just be 0

Answer 2

Using L'hopitals rule

Answer 3

Understand?

Answer 4

note that\[\sin(\frac{1}{x^4+y^4})\]is a limited function between -1 and 1 whatever x,y are so we have a limited function multiplying zero (because y->0) and\[\lim_{(x,y) \rightarrow(0,0)} y \ \sin(\frac{1}{x^4+y^4})=\lim_{y \rightarrow 0} \times\lim_{(x,y) \rightarrow(0,0)} \sin(\frac{1}{x^4+y^4})=0\times \text{limited}=0\]make sense???