lim x->oo (x^2)sin(1/x)

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- May 21st 2007, 06:47 PMjephl`hospital
lim x->oo (x^2)sin(1/x)

- May 21st 2007, 07:01 PMThePerfectHacker
- May 21st 2007, 07:04 PMjeph
are you sure? o.o

the answer my prof provided was oo - May 21st 2007, 07:14 PMThePerfectHacker
I did it for instead of .

In that case,

But we do not need to use that rule.

Instead for sufficiently large consider the reciprocal, i.e.

We can think of this reciprocal function as a composition where and . But at we define to be zero. Why? Because . This makes*continous*at zero.

Now and is continous at 0. By the limit composition rule the limit .

We have shown that . Which implies that its reciprocal is that is, .