Limits of X->0

[DarkestEvil]

. . . . . . . .______ . . . __
Find lim (\/ X + ?X) -( \/ X)
. . .?X->0 -----------------------
. . . . . . . . . . . . ?X

Pay no mind to the periods... dashes = fraction \/ thing = square root
Sorry I couldn't make my problem look fancy. Alright heres the problem I'm having.
I have to find the limit of ?X -> 0 , yet I cannot plug in the value because it will result in a #/0
So I try to plug in a number very close to 0 (0+,0-) such as 0.000001 and -0.000001 to determine whether the infinite value will be positive or negative. But when I try to plug in either values, I'm stumped with both the X and the value of ?X together in the square root, and I get lost. Some help guiding me through this problem would be greatly appreciated.

It also seems I've done this problem incorrectly:

Find lim. . . sin 4X
. . . X->0 -----------
. . . . . . . . . . X

Since I can't plug in 0 for X, I do the same thing as the above, by plugging in values very close to 0, and I end up punching in the equation with the X value equaling 0.00001 and -0.00001, with the sine function and all, and end up with the limit becoming positive infinity. My teacher marked this wrong. I kind of recall there being a rule about limits involving sine and cosine, but I can't remember it.

Also, in case you haven't noticed, im new to this forum, so can someone explain how to make my equations look prettier.

 

[tkhunny]

Well, Darkest, you seem to be missing the point fo this lesson. You would do well to review the material. Limits are likely to be a new concept to you. It is generally a bad idea to bring only old concepts to solve new ideas. However, in this case, we see that a little algebra and trigonometry will save you from the fine art of "plugging in".

On the second, ley's remember some trigonometry. sin(2x) = 2sin(x)cos(x) Use that twice and see what happens.

On the first, you will have to do something that may hurt your feelings. Try rationalizing the NUMERATOR. :shock:

Let's see what you get.