## dgamma3 Group Title How would you solve the following limit: limit (x -> 0+) (x-11)/sin(x) one year ago one year ago

1. dgamma3 Group Title

you can do it manually, and figure out its negative infinity. but is there any algebraic way.

2. dgamma3 Group Title

$\lim_{x \rightarrow 0+} (x-11)/\sin(x)$

3. nitz Group Title

$\lim_{x \rightarrow 0}(sinx/x)=1$

4. kirbykirby Group Title

$You know \lim_{x \rightarrow 0+} \frac{\sin x}{x}=1$

5. kirbykirby Group Title

so: do the same trick I told you before: Divide the top and bottom by x

6. nitz Group Title

and $\lim_{x \rightarrow 0}(11/sinx)\rightarrow \infty$

7. kirbykirby Group Title

$\lim_{x \rightarrow 0+} \frac{\frac{11-x}{x}}{\frac{\sin x}{x}} = \lim_{x \rightarrow 0+} \frac{11/x-1}{\frac{\sin x}{x}}=$$\frac{\infty-1}{1}=\infty$