Limits

**lehder** · August 12th 2009, 05:34 PM

HI,

I didn't knox how to calculate the following limits:

1)- $\lim_{x\to \frac{\pi}{4}} f(x)=\frac{tanx-1}{\sqrt{2}cosx-1}$ .

2)- $\lim_{x\to 0} f(x)=\frac{cosx+cos2x-2}{cos3x+sinx-1}$

Can you help me please?

And Thank's for anyway.

**pickslides** · August 12th 2009, 06:10 PM

Originally Posted by lehder

HI,

I didn't knox how to calculate the following limits:

1)- $\lim_{x\to \frac{\pi}{4}} f(x)=\frac{tanx-1}{\sqrt{2}cosx-1}$ .

Have you herd of L'hospital's rule?

For $\lim_{x\to a} f(x)=\frac{g(x)}{h(x)}$

if $\lim_{x\to a} g(x) = \lim_{x\to a} h(x) = 0$

then $\lim_{x\to a} f(x)=\frac{g(x)}{h(x)} = \lim_{x\to a} f(x)=\frac{g'(x)}{h'(x)}$

**lehder** · August 12th 2009, 06:21 PM

Originally Posted by pickslides

Have you herd of L'hospital's rule?

For $\lim_{x\to a} f(x)=\frac{g(x)}{h(x)}$

if $\lim_{x\to a} g(x) = \lim_{x\to a} h(x) = 0$

then $\lim_{x\to a} f(x)=\frac{g(x)}{h(x)} = \lim_{x\to a} f(x)=\frac{g'(x)}{h'(x)}$

Thank you very much, i find that 1) = -2

**pickslides** · August 12th 2009, 06:25 PM

I agree

**lehder** · August 12th 2009, 06:37 PM

Originally Posted by pickslides

I agree

And the second is egal = 0

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