# Homework Help: Take the limit

1. Feb 28, 2014

### brycenrg

1. The problem statement, all variables and given/known data

2. Relevant equations
How does he get sin(theta)/theta / 1+ sintheta/theta *1/costheta
I don't understand how he goes from sinetheta/theta + tantheta to sin(theta)/theta / 1+ sintheta/theta *1/costheta

to me it looks like he just brought up the theta like theta/1 and just bumped up the theta but i know you cant do that.

3. The attempt at a solution
Ive tried too many times, there is my question if anyone can help. I appreciate it.

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2. Feb 28, 2014

### scurty

1/theta was multiplied in both the numerator and denominator (i.e. Multiplying by 1). It's a type of algebraic manipulation trick, similar to cleverly adding 0 to an expression to simplify it.

3. Feb 28, 2014

### PeroK

Another method: you could try inverting the original limit and see what you get:

$$\lim_{θ→0} \frac{θ+tanθ}{sinθ}$$

4. Feb 28, 2014

### brycenrg

Thank you, I remember that trick. I don't see it though because if you times it by theta/theta wouldn't it be thetasin(theta)/ 2theta + tantheta? Even if i did (1/theta) / (1/theta) its seems not to work because 1/costheta would be 1/theta(cos(theta))..dang i dont see it.

5. Feb 28, 2014

### brycenrg

So i see that it would work for (1/theta)(1/theta) is that what you mean? i mean that is the same thing as theta over theta but you have to put it in that form for it to work

6. Feb 28, 2014

### scurty

Yeah, that's what I mean. The whole point of doing that is so you would have a $\frac{sin(\theta)}{\theta}$ in the expression, which you know the limit of.