## anonymous 5 years ago find the limits when h ->0 h /tan^2h

1. anonymous

h approaches 0 and tan^2h approaches 0 as h approaches 0, so you have an indeterminate form. Use L'Hopital's rule to obtain$\lim_{h \rightarrow 0^+}\frac{h}{\tan^2h}=\frac{\lim_{h \rightarrow 0^+}h}{\lim_{h \rightarrow 0^+}\tan^2h}=\frac{\lim_{h \rightarrow 0^+}1}{\lim_{h \rightarrow 0^+}2\tan (h) \sec^2 h}=\frac{1}{\lim_{h \rightarrow 0^+}2\tan (h) \sec^2 h}\rightarrow +\infty$

2. anonymous

Refresh the screen if it doesn't show up properly.

3. anonymous

where did u get sec

4. anonymous

That's the limit from the right (i.e. heading toward 0 from the positive part of the number line).

5. anonymous

From the derivative of tan(x):$\frac{d}{dx}\tan^2x=2\tan x \sec ^2 x$(chain rule)

6. anonymous

i didnt know u take the derivative

7. anonymous

$\lim_{h \rightarrow 0^-}\frac{h}{\tan^2h}=\frac{\lim_{h \rightarrow 0^-}h}{\lim_{h \rightarrow 0^-}\tan^2h}=\frac{\lim_{h \rightarrow 0^-}1}{\lim_{h \rightarrow 0^-}2\tan (h) \sec^2 h}=\frac{1}{\lim_{h \rightarrow 0^-}2\tan (h) \sec^2 h}\rightarrow -\infty$

8. anonymous

You take the derivative for L'Hopital's rule.

9. anonymous

In its original form, you can't say anything about the limit. Anything where you have$\frac{0}{0}, \pm \frac{\infty}{\infty}$is an indeterminate form (you can't say anything about it). We use (usually) L'Hopital's rule to reduce it into a determinable form.

10. anonymous
11. anonymous

ohhhh,, nice

12. anonymous

so when u do that?

13. anonymous

when u cant do anything about the limit

14. anonymous

If you look above, I tell you when you have an indeterminate form.

15. anonymous

0/0 +/ infty/infty

16. anonymous

ok

17. anonymous

Here, the h in the numerator approached 0 the tan^2h in the denominator approached 0 when h approached 0, so you had a case of 0/0 which is indeterminate.

18. anonymous

You look at the numerator and denominator separately first (i.e. to see if you get an indeterminable form). If it's the case, apply L'Hopital's rule or something else (but no one uses the 'something else').

19. anonymous

jajjaaj

20. anonymous

ok

21. anonymous

:)

22. anonymous

thanks.. very good explanation

23. anonymous

welcome