This one has got me totally stumped:

$\displaystyle

f(x) = \left\{ \begin{array}{rcl}

2x^2 - 3x + 1 & \mbox{} & x<-1 \\ ax +b & \mbox{} & -1\leq x <{2} \\ 8x + 5 & \mbox{} & x \geq {2}

\end{array}\right.$

I've been told to find the values of a and b so f(x) is continous everywhere. I'm not exactly sure of the method used to find the two integers in order to make the piecewise statement true, and therefore continous.

Also, I have these 2 to do as well:

$\displaystyle lim x -> 0 = \frac{tan(4x)}{6x}$

$\displaystyle lim x -> 0 = \frac{(3x - sinx)^2}{x^2}$

I'll probably kick myself whenever I figure the bottom two out. I recall the process being fairly simple, but when you haven't slept in about a day and a half, your brain starts to become a little fuzzy.

Some help on these would be great... I've been working on this worksheet since 12:00.