Question

evaluate lim x-> pi/3 (tanx/x)
Answer=1?

Answer 1

Really? How you got that??

Answer 2

tan(x) at x = pi/3 is a finite value..

x = pi/3 is also finite..

So, you can directly plug in the value of x there..

Answer 3

\[\tan(\frac{\pi}{3}) = ??\]

Answer 4

\[\sqrt{3}\]

Answer 5

Thats the answer?

Answer 6

No...

Answer 7

you have tan(x) divided by x too..

So divide tan(pi/3) with pi/3

Answer 8

\[\lim_{x \rightarrow \frac{\pi}{3}} (\frac{\tan(x)}{3}) \implies \frac{\tan(\frac{\pi}{3})}{\frac{\pi}{3}}\]

Answer 9

Well I did, \[\frac{ \frac{ sinx }{ cosx} }{ x } = \frac{ sinx }{ x }\left[ \frac{ 1 }{ cosx} \right] =1\]

Answer 10

\[\lim_{x \rightarrow \frac{\pi}{3}} (\frac{\tan(x)}{x}) \implies \frac{\tan(\frac{\pi}{3})}{\frac{\pi}{3}}\]

Answer 11

I dont know if what i did is possible.. :p

Answer 12

\[\sin(\frac{\pi}{3}) = ??\]

Answer 13

\[\cos(\frac{\pi}{3}) = ??\]

Answer 14

Wait, the answer is 2?

Answer 15

No.. Why can't you write it properly and check what is the answer you are getting?

Be slow, are you running out of time?

Answer 16

\[\frac{1}{\frac{\pi}{3}} \cdot \frac{\sin(\frac{\pi}{3})}{\cos(\frac{\pi}{3})}\]

Answer 17

Be slow, evaluate this and tell me what did you get..

Answer 18

Wait, I see, are you using this formula:

\[\lim_{x \to 0} \frac{\sin(x)}{x} = 1\]

Answer 19

1.654

Answer 20

yesss, oh it doesn't apply here?

Answer 21

Oh..

Be careful with the Limits given.. You are doing Limits, so you have to fully concentrate on what the limits are.. In this formula, x tending to 0 is must..

But in your original question, x is not tending to 0, are you getting this??

Answer 22

Yes, 1.654 that you got is correct..

Answer 23

Oh yes! I see what i did wrong

Answer 24

Thank youuuuu :D

Answer 25

You are welcome dear.. :)

Answer 26

And for you knowledge:

\[\lim_{x \to 0} \frac{\tan(x)}{x} = 1\]

Answer 27

Again remember, in this x must tend to 0..

Answer 28

Haha, yes!

Answer 29

Okay, that's great. :) Keep it up.. :)

Answer 30

I have another question, its a bit tricky. I'll post it now

Answer 31

Sure..