Squeeze theorem

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

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

squeeze it.
October 8th 2009, 07:17 PM
math123456

squeeze theorem

I am not sure what you mean by this. Can you help me solve it.
October 8th 2009, 07:43 PM
mr fantastic

Quote:

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.

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 ....

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