Question

lim x tanx/ 1-cosx
x―>0

please help...

Answer 1

Try multiplying the numerator and denominator by 1+cosx. See if you can solve it using that.

Answer 2

xtan x(1+cos x)/1-cos x)(1+cos x)

Answer 3

then xtanx/sin^2x

Answer 4

div by x^2 in num and denominator

Answer 5

(You forgot the 1+cosx factor in the numerator, AvarindG)

Answer 6

srry ringlum

Answer 7

wel katy i suggest u work out rest and a[ply limits .u will get it

Answer 8

okie....thank u both...i got stuck wid the div part.. :)

Answer 9

It's ok. In general for limits involving trigonometric functions, keep in mind the identities you know. In this case, it was useful to remember that
\[1 - \cos^2(x) = \sin^2(x)\]
Therefore prompting one to multiply the denominator and numerator by \[1+\cos(x)\] in order to get that.

Answer 10

thank you...:)

Answer 11

when x = 0 the function becomes 0 / 0 ie indeterminate

so it might be a good idea to use l'hopitals rule

so differentiate top and bottom

Answer 12

i haven't studies L Hospital rule yet.. i dont know that..:(

Answer 13

f'(x) = ( x sec^2 x + tan x) / sin x

Answer 14

oh ok

Answer 15

Actually, it's not necessary to apply l'Hopital's rule. you have

x(1 + cos x)tan x / sin^2 x.

Now as tan x = sin x / cos x, you can cancel one term of sin x in numerator and denominator. Now bring the x into the denominator and you have
\[ \frac{(1 + \cos x)\cos x }{(\sin x)/x} \]
Now the limit as x --> 0 of sin x / x is 1. Hence you should now now be able to evaluate the limit.

Answer 16

so answer is 2?

Answer 17

Yes

Answer 18

thank you..

Answer 19

can we do
lim (tan 7x-3x/7x-sin^2 x)
x->0
in the same way?

Answer 20

please tell me what all identities should i use?

Answer 21

Could you write that using the "Equation" functionality here? It makes it easier to read. Right now it's confusing as there could be parenthesis missing.

Answer 22

okie..

Answer 23

\[\left[\begin{matrix}\tan 7x & -3x \\ 7x- & \sin^2x\end{matrix}\right]\]

Answer 24

Uhm... xD

Answer 25

Don't think that's what you meant.

Answer 26

there is a division in the middle.i coudnt get it..

Answer 27

\[(\tan(7x)-3x)/(7x-\sin^2(x))\] is that it?