Finding limits

1. Nov 3, 2013

physics604

1. lim θ→0 $\frac{sinθ}{θ+tanθ}$

2. Relevant equations

lim x→0 $\frac{sinx}{x}$=1

lim x→0 $\frac{cosx-1}{x}$=0

3. The attempt at a solution

lim θ→0 $\frac{sinθ}{θ+sinθ/cosθ}$

lim θ→0 $\frac{sinθ}{(θcosθ+sinθ)/cosθ}$

lim θ→0 sinθ × $\frac{cosθ}{θcosθ+sinθ}$

lim θ→0 $\frac{θcosθ}{θcosθ+sinθ}$

The answer is supposed to be $\frac{1}{2}$. What did I do wrong?

2. Nov 3, 2013

Dick

You haven't done anything wrong yet. You just aren't finished. Now divide numerator and denominator by θ and let θ go to zero.

3. Nov 3, 2013

Student100

Have you covered L'Hospital's rule?

4. Nov 3, 2013

Dick

Likely not, since the ingredients are the elementary trig limits.

5. Nov 3, 2013

physics604

Not in class, but I know that it's a quick way to solve limits. Meaning the derivative of the top divided by the derivative of the bottom.

6. Nov 3, 2013

physics604

I can't divide divide numerator and denominator by θ... If θ went to zero then that would make my denominator zero, which would be undefined.

7. Nov 3, 2013

physics604

Nevermind, I got it! Thanks!

8. Nov 3, 2013

Student100

Yeah, I shoulda picked up on that!

Anyways, looks like you solved their problem Dick!

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