Understanding Limits: Evaluating Tricky Expressions

[johnq2k7]

2.) Evaluate the following limits, justifying your answers. If a limit does not exist explain why.

a.) lim (x--> inf.) (3x^3 +cos x)/(sin x- x^3)


b.) lim (x-->Pie(+)) (tan^-1 (1/(x-Pie)))/(Pie-x


I have no idea, what do here please help me with these problems!

 

[Mark44]

For a, factor x^3 from both terms in the numerator and both terms in the denominator.
For b, if I'm interpreting what you wrote correctly, the numerator is approaching pi/2 (note spelling -- the name of this Greek letter is pi, not pie), and the denominator is approaching 0, so the quotient is getting large without bound.