Question

20 Points. Precalc help!
Find the limit of the function algebraically.

Answer 1

The limit does not exist. For small enough
`x<0` we have
`x^3+1>0` and
`x^5<0`, while for small enough
`x>0` we have
`x^3+1>0` and
`x^5>0`. This means to the left, the limit has negative sign, and to the right, the limit has positive sign. Direct substitution gives the undefined
`\frac10` which indicates the limit is infinite, but the sign changes depending on the direction.