Question

Question #0138c

Answer 1

`lim_(x->0)frac{1}{sin^3x-1/(x^3)}=0`

Explanation:

`lim_(x->0)frac{1}{sin^3x-1/(x^3)}`

Multiply the fraction by `color(blue)(frac{x^3}{x^3})` to get
`lim_(x->0)frac{x^3}{x^3sin^3x-1}`

By direct substitution, this gives:
`frac{color(red)(0)^3}{color(red)(0)^3sin^3 color(red)(0)-1}=0/-1 =0`

`:. lim_(x->0)frac{1}{sin^3x-1/(x^3)}=0`