zhiyuan3yu5 2 years ago find limit of ysin(1/(x^4+y^4)) as (x,y)--->(0,0)

1. WhiiteRussian

It would just be 0

2. WhiiteRussian

Using L'hopitals rule

3. WhiiteRussian

Understand?

4. mukushla

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???