dgamma3 3 years ago How would you solve the following limit: limit (x -> 0+) (x-11)/sin(x)

1. dgamma3

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

2. dgamma3

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

3. nitz

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

4. kirbykirby

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

5. kirbykirby

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

6. nitz

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

7. kirbykirby

$\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$