help on these five calculus problems

[notmathsavvy]

the notation was difficult to write out so i thought i'd just take a screenie and post the link to it.

http://i50.tinypic.com/2duh4iq.png

any help on any of the problems would be much appreciated!

 

[notmathsavvy]

eliminate 2 and 3 i got those now.

edit: also 5

 

[HallsofIvy]

So 1 and 4 are the only ones you are having trouble with?

For 1, the obvious first step is to "rationalize the numerator" by multiplying both numerator and denominator by \(\displaystyle \sqrt{ax+b}+ 2\). Because of that "x" in the denominator (you obviously don't want x, going to 0, in the denominator) you will have to have an "x" in the numerator to cancel it.

For 4: Leibniz's formula: \(\displaystyle \frac{d}{dx}\int_{\alpha(x)}^{\beta(x)} F(x, t)dt= F(x,\beta(x))\frac{d\beta}{dx}- F(x,\alpha(x))\frac{d\alpha(x)}{dx}+ \int_{\alpha(x)}^{\beta(x)} \frac{\partial F(x,t)}{\partial x}dt\).