Answer to Question #288855 in Calculus for Pankaj

Question #288855

lim x ➡0 (lim y ➡0 for ysinx/|x|) does not exist. Say true or false


1
Expert's answer
2022-01-24T17:04:28-0500
limx0(limy0ysinxx)limx0(limy00sinxx)limx0(limy00x)limx0(limy00)limx0(0)limx00=0\lim_{x \rightarrow 0 } \bigg(\lim_{y \rightarrow 0 } \frac{y \sin x}{|x|}\bigg)\\ \lim_{x \rightarrow 0 } \bigg(\lim_{y \rightarrow 0 } \frac{0 \cdot \sin x}{|x|}\bigg)\\ \lim_{x \rightarrow 0 } \bigg(\lim_{y \rightarrow 0 } \frac{0 }{|x|}\bigg)\\ \lim_{x \rightarrow 0 } \bigg(\lim_{y \rightarrow 0 } 0 \bigg)\\ \lim_{x \rightarrow 0 } \big(0 \big)\\ \lim_{x \rightarrow 0 } 0 =0\\

Therefore,


limx0(limy0ysinxx)=0\lim_{x \rightarrow 0 } \bigg(\lim_{y \rightarrow 0 } \frac{y \sin x}{|x|}\bigg) =0\\

and thus exist (FALSE)


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog