Please help me solve lim (sin 2x)/x

x approaching zero.

I'm supposed to determine the limit graphically and then confirm algebraically.

Thank you.

Printable View

- October 1st 2008, 11:44 PMmacgyverLimits and Continuity
Please help me solve lim (sin 2x)/x

x approaching zero.

I'm supposed to determine the limit graphically and then confirm algebraically.

Thank you. - October 1st 2008, 11:49 PMChris L T521

Here's the graph:

http://img.photobucket.com/albums/v4...T521/limit.jpg

Can you determine now?

Here's a hint on how to verify it algebraically.

This limit should look pretty familiar...

Does this help?

--Chris - October 1st 2008, 11:50 PMwisterville
Hello,

I don't know what you mean by "graphically"(draw a graph? computing areas?).

For the "algebraically" one, do you know lim((sin x)/x)=1?

If so, transform as (sin 2x)/x=2(sin 2x)/(2x) and let 2x go to 0.

Bye.

P.S. Seems I was slower than Chris. - October 2nd 2008, 12:06 AMmacgyver
Thank you very much for responding Chris. I only get part of it though. could you please tell me how to determine the limit just by looking at the graph? and also how do I solve the rest of the equation. I am very new to calculus so I would really appreciate your help.

- October 2nd 2008, 12:11 AMChris L T521
To find the limit graphically, look at the value of the graph at . In this case it appears to be 2, although it doesn't exist at 0 [otherwise we would be dividing by zero, which is illegal].

To finish it off, this is what we would do algebraically:

This limit has the form of

So let . Thus, as , as well.

So our limit transforms from to

Does this make sense?

--Chris - October 2nd 2008, 12:25 AMmacgyver
yes thank you that helped a lot.

could u help me with this other one please?

f(x)=(e^-x)/(x)

I'm supposed to

a: use graphs and tables to find lim x approaching infinity f(x)

b: lim x approaching negative infinity f(x)

c: Identify all horizontal asymptotes