- #1

duki

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## Homework Statement

Have a couple of questions actually.

Problem #1 [tex]\lim_{x\rightarrow 0}{\left(\frac{4x}{\sin 5x}\right)}[/tex]

## Homework Equations

I was told in class to do [tex]\lim_{x\rightarrow 0}{\left(\frac{4x*5}{5\sin 5x}\right)}[/tex]

## The Attempt at a Solution

so after that I was told that [tex]{\left(\frac{x}{\sin x}\right)} = 1[/tex]

but my book says [tex]{\left(\frac{x}{\sin x}\right)} = 0[/tex]

The final answer we were given was [tex]4/5[/tex]

Could someone explain this to me? I know how he got 4/5, but which sin formula is correct?------------------

Problem #2 [tex]\lim_{x\rightarrow 0}{\left(\frac{1-\cos x}{x^2}\right)}[/tex]

I can get to this step:

[tex]\lim_{x\rightarrow 0}{\left(\frac{\sin^2 x}{\left(1+\cos x\right)x^2}\right)}[/tex]

but what's next?

Thanks guys! I have a test tomorrow, so I'm just trying to get some things straight