What is the limit of xsqrt(sin1/x) as x approaches zero?

Question

And also as x approaches zero along the domain of the above function. Thanks in advance!

Answer 1

There is a problem: as sin1/x as x ===>0 is negative at an infinite
number of points as near as you wish to zero.At those points sqrt sin1/x does not exists.
For the definition of limit there must be an environment of the point, in this case 0,where the function exists(except 0)

In this case this environment does not exist so the limit DOES NOT EXIST.

I Think that you are supposed to say that as -1<=sqrtsin1/x)<=1
so this function is limited below and above,multplied by x ===>0
the limit is zero but this is wrong