Question

Question #db808

Answer 1

`0`

Explanation:

(x^(-4/3))/sin(1/x) = `(x^(-1/3)*x^-1)/sin(1/x) =1/x^(1/3) (1/x)/sin(1/x)`

As `xrarroo`,

`1/x^(1/3) rarr 0` and

`1/x rarr 0` so `(1/x)/sin(1/x) = 1`

Therefore,

`lim_(xrarroo)x^(-4/3)/sin(1/x) =0`