Question

limit as x approaches 0 of sin(x)/x^2-x

Answer 1

limit as x approaches 0 for:

\[\sin (x) \div x^2-x\]

Answer 2

Use L'Hopital's rule. Are you familiar with that?

Answer 3

i think i've heard it before, however, i don't know what it is

Answer 4

If you have a limit where both the numerator and denominator = 0 when you plug in the number your limit is approaching, then you can take the derivative of the numerator and the derivative of the denominator separately and try plugging in the number your limit is approaching again.

Answer 5

i'm still in pre-calculus and we haven't learnt derivatives yet...

Answer 6

Then this problem is ugly. Sorry can't help.

Answer 7

haha it's fine, thanks for trying

Answer 8

\[\lim_{x \rightarrow 0}\frac{ \sin x }{ x ^{2} }-x \text{, like this?}\]

Answer 9

nope, the -x is in the denominator, next to \[x^2\]

Answer 10

so it's \[x^2-x\] in the denominator

Answer 11

okay... then factor
\[\lim_{x \rightarrow 0}\frac{ \sin x }{ x ^{2}-x }=\lim_{x \rightarrow 0}\frac{ \sin x }{ x \left( x-1 \right) }=\lim_{x \rightarrow 0}\frac{ \sin x }{ x }\frac{ 1 }{ \left( x-1 \right) }\]
sin x/x goes to 1 and 1/(x-1) goes to -1 so take the product of the 2

Answer 12

oh! thank you so much! this makes sense now, i never thought to factor it! thanks :)

Answer 13

you're welcome!!!