Limits- using L'hopital's rule

1. Apr 4, 2010

Jenkz

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

Lim tan (x^1/2)/ [x (x+1/2)^1/2 ]
x-> 0

3. The attempt at a solution

I have attempted to differentiate both the denominator and numerator seperately but this just seems to complicate the whole equations and I still get a limit of 0.

I had an idea to square everything, in which case I get a limit of 1. However, I do not think [tan (x^1/2)]^2 = tanx

Please help? My friend and I have been trying to work this out. It isn't homework, merely revision and further understanding.

2. Apr 4, 2010

willem2

You must have made an error while differentiating, the limit is not 0.

[tan (x^1/2)]^2 is not the same as tanx. Try $x = \pi$

3. Apr 4, 2010

Jenkz

My mistake, the equation is

tan (x^1/2)/ [x (1+1/x)^1/2 ] sorry

I'll try your hint, and have another go at differentiating it. Thanks.

4. Apr 4, 2010

Staff: Mentor

Minor point - that's not an equation. They're easy to spot because there's one of these- = - in an equation.

5. Apr 5, 2010

Jenkz

@Mark44: okies, noted.

I've tried differentiating it again and I get:

$$\frac{\frac{sec^{2}\sqrt{x}}{2\sqrt{x}}}{\sqrt{\frac{1}{x}+1}-\frac{1}{2\sqrt{\frac{1}{x}+x}}}$$

But it still doesn't give me a limit.

I'm not too sure how to use your hint. As if i let $$\pi=x$$ Doesnt it just mean $$\pi$$ tends towards 0 instead of x ?

Confused...

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