Question

find the limits when h ->0 h /tan^2h

Answer 1

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\[\lim_{h \rightarrow 0^+}\frac{h}{\tan^2h}=\frac{\lim_{h \rightarrow 0^+}h}{\lim_{h \rightarrow 0^+}\tan^2h}=\frac{\lim_{h \rightarrow 0^+}1}{\lim_{h \rightarrow 0^+}2\tan (h) \sec^2 h}=\frac{1}{\lim_{h \rightarrow 0^+}2\tan (h) \sec^2 h}\rightarrow +\infty\]

Answer 2

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

Answer 3

where did u get sec

Answer 4

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

Answer 5

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

Answer 6

i didnt know u take the derivative

Answer 7

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

Answer 8

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

Answer 9

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.

Answer 10

Here:

http://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule

Answer 11

ohhhh,, nice

Answer 12

so when u do that?

Answer 13

when u cant do anything about the limit

Answer 14

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

Answer 15

0/0
+/ infty/infty

Answer 16

ok

Answer 17

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.

Answer 18

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').

Answer 19

jajjaaj

Answer 20

ok

Answer 21

:)

Answer 22

thanks.. very good explanation

Answer 23

welcome