Help with Limits

[johnny101]

Can someone show how to solve this? Note, the possibility of not enough information as an answer has been included for every text problem including this one.

Find the limit L, if the limit x(approaches 0)g(x)=0, and g(x) does not equal 0 in an open interval I containing the point x=c except possibly itself, then the limit

x(approaches 0) sin g(x)/g(x)= L..

..How the heck do I solve this? Step-by-step help would be appreciated!

 

[stapel]

Find the limit L, if the limit x(approaches 0)g(x)=0, and g(x) does not equal 0 in an open interval I containing the point x=c except possibly itself, then the limit

x(approaches 0) sin g(x)/g(x)= L..

For clarity, is the limit expression meant to be as follows?

. . . . .\(\displaystyle \mbox{If }\, \displaystyle{\lim_{x\, \rightarrow\, 0}\, g(x)\, =\, 0, }\, \mbox{ then find }\, L\, \mbox{ for}\)

. . . . . . . . .\(\displaystyle \displaystyle{\lim_{x\, \rightarrow\, 0}\, \frac{\sin(g(x))}{g(x)}\, =\, L}\)

How the heck do I solve this?

They're probably expecting you to remember a limit that didn't seem that "important" way back when they covered it:

. . . . .\(\displaystyle \displaystyle{\lim_{\theta\, \rightarrow\, 0}\, \frac{\sin(\theta)}{\theta}\, =\,1}\)

Apply this limit, and you're home and dry! :wink:

 

[johnny101]

For clarity, is the limit expression meant to be as follows?

. . . . .\(\displaystyle \mbox{If }\, \displaystyle{\lim_{x\, \rightarrow\, 0}\, g(x)\, =\, 0, }\, \mbox{ then find }\, L\, \mbox{ for}\)

. . . . . . . . .\(\displaystyle \displaystyle{\lim_{x\, \rightarrow\, 0}\, \frac{\sin(g(x))}{g(x)}\, =\, L}\)


They're probably expecting you to remember a limit that didn't seem that "important" way back when they covered it:

. . . . .\(\displaystyle \displaystyle{\lim_{\theta\, \rightarrow\, 0}\, \frac{\sin(\theta)}{\theta}\, =\,1}\)

Apply this limit, and you're home and dry! :wink:

The limit is correct as you have it yes. I tried solving it with that actually but the answer I get doesn't match any of the text options..could u walk me through that conversions?

 

[stapel]

The limit is correct as you have it yes. I tried solving it with that actually but the answer I get doesn't match any of the text options..could u walk me through that conversions?

What "options" have you been given? What "answer" do you get?

Please show all your steps. Thank you!

 

[johnny101]

the options are L=0, 1, g(x), or none of those or not enough information.

I understand the sin conversion equals 1, but how do I plug that back into the equation?

Thats where i get lost specifically.

 

[stapel]

What do they give you as the limit, as x tends to zero, of g(x)? ;-)