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I am having difficulties with two limit problems and hopefully someone can show me a trick or two that I don't know!

1) find [tex]\lim_{x\rightarrow 0}\frac{sin^{2}(\frac{x}{2})}{sin(x)}[/tex]

Is it just me or is this thing a beast of a limit. I just can't get the denominator to equal anything other then 0!

I tried using the half angle identity on the top but it simply doesn't help...

2)find [tex]\lim_{x\rightarrow \frac{\pi}{4}}\frac{1-tan(x)}{sin(x)-cos(x)}[/tex] This one I don't even know where to start, I know that I need to get 1-cos(x)/x or cos(x)-1(x) and/or sin(x)/x or x/sin(x)... but I don't see a way.

PS- thats x approaches x/2(not pi....) sigh (for q1) and PI/4 (for q2) btw. it's small. :(

Help!

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# Homework Help: Two limit problems

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