# What are the LIMITS of these functions?

• Sep 23rd 2010, 06:46 PM
What are the LIMITS of these functions?

What is the limit of sin(x) as x is approaching infinity?

Also, what is the limit of tan(x) when x is approaching pi from the right? (RIGHT HAND LIMIT)

Last, what is the limit of tan(x) when x is approaching to pi?

And last one, what is the limit of f(x) (4/x , x less than 1) and (x^3 - 2x + 5 , x greater than 1.) This function is probably peicewise.

Thank you very much.

Thank you!
• Sep 23rd 2010, 07:35 PM
Prove It
$\lim_{x \to \infty}\sin{x}$ does not exist, because the function continues to oscillate around $[-1, 1]$.

$\lim_{x \to \pi}\tan{x} = \lim_{x \to \pi}\frac{\sin{x}}{\cos{x}}$

$=\frac{\sin{\pi}}{\cos{\pi}}$

$=\frac{0}{1}$

$=0$.

This is the same coming from the right and the left.

$\lim_{x \to 1}f(x)$ where $f(x) = \begin{cases}\frac{4}{x} \textrm{ if }x<1\\ x^3 - 2x + 5\textrm{ if }x>1\end{cases}$?
To evaluate that limit, if it exists, work out what the function approaches from the left (when $x < 1$) and what the function approaches from the right (when $x >1$. If they are the same, then the limit exists and is this value.