Question

Can you help me find this limit: http://screencast.com/t/6CD9ErAG3N9m

All I need is the first step, I am gonna climb from there easily. Sorry if it's a little unclear picture, it's from an old book

Answer 1

@ganeshie8 @Mertsj

Answer 2

for reference, the answer is \[-\sqrt3/2\] i do not remember the steps though, sorry

Answer 3

I know the answer too my friend, but I dont know how to find it, thanks though

Answer 4

sorry i could not help :/

Answer 5

CANT EVEN SEE THE QUESTION

Answer 6

How Come?? The guy above you saw it , I posted a picture

Answer 7

I can't see it either. what is the limit going to? Can't make it out after the arrow

Answer 8

infinity+ ....

Answer 9

+ infinity ***** I am sorry

Answer 10

lim of x going to positive infinity of sin((pi*x)/(2-3x))

Answer 11

\[\lim_{x \rightarrow +\infty}\sin (\frac{ \pi x }{ 2-3x })\]

Answer 12

can you actually take the pic clearly?

Answer 13

\[\lim_{x \rightarrow +\infty} Sin (\frac{ \pi x }{ 2-3x })\]

Answer 14

Yes

Answer 15

Now Stewie can stop trolling, lol. xD

Answer 16

VICTORY?

Answer 17

I want to learn this too

Answer 18

Same here.

Answer 19

yes or no?

Answer 20

who is teaching??

Answer 21

You can divide by the highest power in the denominator which is x

Answer 22

But how does that lead you to the solution which is -sqrt(3)/2

Answer 23

Can't you? \[\large \lim_{x \rightarrow +\infty}\sin(\frac{ \pi x/x }{ \frac{ 2 }{ x }-\frac{ 3x }{ x } })\]

Answer 24

yes and then?

Answer 25

So what is \[\sin(-\frac{ \pi }{ 3 })\]? Whcih quadrant is sine negative ?

Answer 26

\[\lim_{x \rightarrow +\infty} \sin \frac{ x }{ x }(\frac{ \pi }{ \frac{ 2 }{ x } - 3 })\]

Answer 27

@myko @timo86m @jim_thompson5910 @jhonyy9 @Hero @Euler271

Answer 28

The result is most likely engative yea

Answer 29

Sin (- pi / 3)

Answer 30

negative*

Answer 31

yes but HOW @rajee_sam

Answer 32

Sine is negative in quadrant 3 and 4, so if \[\sin \frac{ \pi }{ 3 } = \frac{ \sqrt{3} }{ 2 }\] then \[\sin -\frac{ \pi }{ 3 }= -\frac{ \sqrt{3} }{ 2 }\]

Answer 33

Am I eligible to differantiate this thing ? because if we differantiate we get sin(pi/-3)

Answer 34

instantly

Answer 35

You just need to find the positive radian measure, which is \[\frac{ \pi }{ }\] and then translate it accordingly to find which negative value is correlated with the positive radian measure

Answer 36

\[\sin ( -\theta ) = - \sin (\theta)\]

Answer 37

sorry,i meant pi/3 *

Answer 38

how did you get the x out @rajee_sam

Answer 39

I am taking a GCF for both numerator and denominator so that I can cancel them out and do not have any x multiplied with anything

Answer 40

GCF ?

Answer 41

Common Factor

Answer 42

\[\lim_{x \rightarrow +\infty}\sin \left(\frac{ \pi x }{ 2-3x }\right) = \sin\left( \lim_{x \rightarrow +\infty} \frac{ \pi x }{ 2-3x }\right)\]
as noted above you can rewrite
\[ \frac{ \pi x }{ 2-3x } = \frac{ \pi }{\frac{2}{x} -3} \]

Answer 43

Alright! Alright! I solved it this way!

By during the time I was trying to solve this I figured out a second way!

Tell me if this is correct:

Just taking the derivative of both denominator and numerator and then we are done. Can I apply this to ANY limit? Because here it works!

Answer 44

that's what i did pi.... :(

Answer 45

@phi

Answer 46

if you're taking the derivative you'll have to use chain rule on the whole thing, sin (whatever's inside) and then * whatever is inside.

Answer 47

yes, you can use L'Hopital's rule
http://en.wikipedia.org/wiki/L'Hôpital's_rule
if you get 0/0 or inf/inf

Answer 48

and no chain rule??

Answer 49

I am talking about this specific problem

Answer 50

no, use chain rule. use
\[ \lim_{x \rightarrow +\infty}\sin \left(\frac{ \pi x }{ 2-3x }\right) = \sin\left( \lim_{x \rightarrow +\infty} \frac{ \pi x }{ 2-3x }\right) \]

Answer 51

*do not use chain rule

Answer 52

but even if I dont use the chain rule we end up to the same result

Answer 53

Ohh so this formula you showed to me just now is only when we have 0/0 or infinite/infinite ?

Answer 54

Oh I see, and you'd use LH rule to simplify it further and end up with the same result.

Answer 55

using L'Hopital's rule needs 0/0 or inf/inf
use it on
\[ \lim_{x \rightarrow +\infty} \frac{ \pi x }{ 2-3x } \]

Answer 56

ok and I get this http://screencast.com/t/jPlMQFrZ

What now?

Answer 57

you can use L'Hopital d top/ d bottom = pi/-3

or you can use algebra

Answer 58

and the lim(x-->+infinity) goes away?

Answer 59

oh I get you now