Question

what is lim sin^-1 (2x)/tan^-1(3x) ???
x->0

Answer 1

http://www.wolframalpha.com/input/?i=limit+of+arcsin%282x%29%2Farctan%283x%29+as+x+approaches+0

Answer 2

remember to click show steps

Answer 3

You have to take the derivative, then do some simplifying

Answer 4

l'hopital's rule

Answer 5

∞ isnt an option m8 ...
its a multiple choice question
A- )2/3 B-)3/2 C-) 0 D-) -2/3

Answer 6

Quake, I gave you a link to the answer as well as the steps, did you look at it?

Answer 7

i am looking right now sounds helpfull

Answer 8

btw lalaly (sin^-1 (2x))' = dx/(1-4 X^2)^(1/2) // right ? check it out for me plz

Answer 9

got u thx.

Answer 10

@quakeash Use this property to find the limit easily
\[\lim_{x\to 0} \frac{\sin ^{-1} x}{x}=\lim_{x\to 0} \frac{\tan^{-1} x}{x}=1\]

Answer 11

omg, ash is smarter than lana

Answer 12

plz inky this is not IQ test , actually i think all mathematics is just about who knows more.. :P

Answer 13

No, I mean, @quakeash , ash just showed the fastest way to get the answer

Answer 14

\[\lim_{x \to 0} \frac{\sin^{-1} 2x}{\tan^{-1} 3x}\]
\[\large \lim_{x \to 0} \frac{\frac {\sin^{-1} 2x}{2x}}{\frac{\tan^{-1} 3x}{3x}}\times \frac {2x}{3x}\]
\[\large \lim_{x\to 0} \frac{1}{1} \times \frac{2x}{3x}=\frac {2}{3}\]
@inkyvyod @lalaly is the smartest

Answer 15

so we divide the numerator and denominator by x right ash ?

Answer 16

oh thx man

Answer 17

No, I'm the smartest *trolololl*

Answer 18

Actually, we don't even need l'hospital. Ash's method is the simplest in the current situation.

Answer 19

it would be so nice if i could use ur help , while taking the exam 2moro :DD

Answer 20

Alas! but we don't help during exams.

Answer 21

@apoorvk , actually, we do, but lol

Answer 22

We just aren't supposed to, and we will stop once we realize what we are doing.

Answer 23

i wont tell u i am taking the exam , ill just use U :P kidding

Answer 24

hehhe, we just won't help you tomorrow muahhaha

Answer 25

@lalaly @quakeash Always nice to know more than one way !!!

Answer 26

@lalaly , there's actually a third way. The fool's way

Answer 27

http://www.wolframalpha.com/input/?i=+arcsin%282x%29%2Farctan%283x%29+with+x%3D0.00000000000000000000000000000000000000000000000000001

Answer 28

\[\text{But since I can't give another medal,} \mathbb{\color{#15B4DC}{@lalaly}} ---> \huge\color{gold}{★} \normalsize \]

Answer 29

Any other ideas?

Answer 30

@lalaly

Answer 31

@apoorvk WOW :D this is better that any medal i got since i joined os :D

Answer 32

Lol.

Answer 33

to make it even better...here's a smiley stamp for you @lalaly \[\huge \color{forestgreen}{\ddot \smile}\]

Answer 34

aww i feel loved ... thanks ewgee <3

Answer 35

you are :P and \[\huge \color{maroon}{\mathtt{\text{<tips hat>}}}\]