Squeeze theorem

**math123456** · October 8th 2009, 03:37 PM

Use the squeeze theorem to solve the limit.

limit when x approaches 0

x^4 cos (3/x)

**skeeter** · October 8th 2009, 04:43 PM

Originally Posted by math123456

Use the squeeze theorem to solve the limit.

limit when x approaches 0

x^4 cos (3/x)

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

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

squeeze it.

**math123456** · October 8th 2009, 07:17 PM

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

**mr fantastic** · October 8th 2009, 07:43 PM

Originally Posted by skeeter

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

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

squeeze it.

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 ....

Thread: Squeeze theorem