Question

How can I work out this: lim x-> 0 (xsinx)/(abs(x)) , not sure what to do with the absolute

Answer 1

use one-sided limits

Answer 2

Is there a way to do it algebraically?

Answer 3

For instance
\[ \large \lim_{x\to0+}\frac{s\sin x}{|x|}=\lim_{x\to0+}\frac{x\sin x}{x}=
\lim_{x\to0+}\sin x=0 \]

Answer 4

Would the squeeze theorum work here?

Answer 5

oh neat, and this would be the limit for the answer? or do i have to find the one of the left as well?

Answer 6

do the left side.

Answer 7

lim x-> 0-
(xsinx)/-x = -0 = 0

Answer 8

does that make sense

Answer 9

yes

Answer 10

oh nice thanks

Answer 11

u r welcome