- #1
Sheepwall
- 15
- 0
Homework Statement
"Calculate the following limit if it exists. If it does not exist, motivate why.
[itex] \displaystyle\lim_{x\rightarrow 0} {\frac{x + x^2 +\sin(3x)}{tan(2x) + 3x}} [/itex]
Do not use l'Hôpital's rule."
Homework Equations
[itex](1) \sin(a\pm b) = \cos(a)\sin(b)\pm\cos(b)\sin(a) [/itex]
[itex](2) \cos(a\pm b) = \cos(a)\cos(b)\mp\sin(a)\sin(b) [/itex]
[itex](3) \displaystyle\lim_{x\rightarrow 0} {\frac{\sin(x)}{x}} = 1 [/itex]
[itex](4) \tan(x) = \frac{\sin(x)}{\cos(x)} [/itex]
The Attempt at a Solution
I have tried expressing the trigonometrics in terms of [itex]\sin(x)[/itex] and [itex]\cos(x)[/itex], but it just got messier without helping me in any way.
This isn't me just jumping on these forums as soon as I can't find the answer; I have genuinely been trying to solve this problem and looking over my methods much more than once.
Thanks in advance!
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