Question

How do you find the limit `(x^3+4x+8)/(2x^3-2)` as `x->1^+`?

Answer 1

`+oo`

Explanation:

use direct substitution:

`lim_(xrarr1^(+))(x^3+4x+8)/(2x^3-2)`

`=((1^(+))^3+4(1^(+))+8)/(2(1^(+))^3-2)`
(`1^(+)` means a number slightly larger than 1, such as 1.0000001)

`=(1^(+)+4^(+)+8)/(2(1^(+))-2)`

`=(13^(+))/(2^(+)-2)`

`=(13^(+))/(0^(+))`

`=+oo`

graph{(x^3+4x+8)/(2x^3-2) [0.9, 1.1, -1000, 1000]}
from the graph, you can see that the function approaches `+oo` as x approaches 1 from the right side