trig limits

[covert flicker]

How to compute this? $\lim_{x\to0}\frac{x^2}{secx-1}$

[muted bronze]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with: ```diff
   +close

[ornate sage]

Anonymous_H

[unique locust]

Apply l'hopital twice?

[covert flicker]

We aren't allowed to use that

[valid robin]

$\lim_{x\to0}\frac{1-cosx}{x} = 0$

[ornate sage]

Ky

[valid robin]

use this property

[polar pumice]

multiply by (sec(x)+1)/(sec(x)+1)
x²(sec(x)+1)/(sec²(x)-1)
then use the identity
sec²(x)-tan²(x) = 1
=> sec²(x)-1 = tan²(x)
after that
x²(sec(x)+1)/tan²(x)
we know that
lim tan(x)/x = 1
x->0
therefore
1×(sec(x)+1) = sec(x)+1
lim sec(x)+1 = sec(0)+1 = 1+1 = 2
x->0

[covert flicker]

It doesnt work

[valid robin]

is the answer 0?

[covert flicker]

oh ok

the answer was 2

[valid robin]

ohk

[covert flicker]

do you mind helping me with this as well?

$\lim_{x\to0}\frac{sin(cosx)}{secx}$

[ornate sage]

Anonymous_H

[covert flicker]

oh wait im so dumb

I got it

tysm!

[polar pumice]

urwelcome

[ruby citrus]

+close