# Squeeze theorem

Printable View

• Oct 8th 2009, 03:37 PM
math123456
Squeeze theorem
Use the squeeze theorem to solve the limit.

limit when x approaches 0

x^4 cos (3/x)
• Oct 8th 2009, 04:43 PM
skeeter
Quote:

Originally Posted by math123456
Use the squeeze theorem to solve the limit.

limit when x approaches 0

x^4 cos (3/x)

since $\displaystyle -1 \le \cos\left(\frac{3}{x}\right) \le 1$ and $\displaystyle x^4 \ge 0$ ,

$\displaystyle x^4(-1) \le x^4 \cos\left(\frac{3}{x}\right) \le x^4(1)$

squeeze it.
• Oct 8th 2009, 07:17 PM
math123456
squeeze theorem
I am not sure what you mean by this. Can you help me solve it.
• Oct 8th 2009, 07:43 PM
mr fantastic
Quote:

Originally Posted by skeeter
since $\displaystyle -1 \le \cos\left(\frac{3}{x}\right) \le 1$ and $\displaystyle x^4 \ge 0$ ,

$\displaystyle x^4(-1) \le x^4 \cos\left(\frac{3}{x}\right) \le x^4(1)$

squeeze it.

Quote:

Originally Posted by math123456
I am not sure what you mean by this. Can you help me solve it.

What is the limit of each side as x --> 0? Therefore ....