Posted by **Bruce** on Wednesday, February 19, 2014 at 1:30pm.

What is the lim of the square root of x times sin of (1/x) as x approaches infinity

- Calc 2 -
**Damon**, Wednesday, February 19, 2014 at 1:52pm
x^.5 * sin (1/x)

as 1/x ---> 0 , sin (1/x) = 1/x

x^.5 * x^-1 = x^-.5 = 1/sqrt x

which = 0 as x ---> infinity

- Calc 2 -
**Steve**, Wednesday, February 19, 2014 at 1:57pm
or, by this time you have probably seen L'Hospital's Rule, so

limit √x sin(1/x)

if u = 1/x, then we have

limit sin(u)/√u

= limit cos(u)/(1/2√u)

= limit 2√u cos(u) as u->0

= 0

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