Question

How do you evaluate the limit x 3 + 1 x + 1 as x approaches 2 ?

Answer 1

`11`

Explanation:

`"assuming you mean"`

`lim_(xto2)x^3+x+1`

`"polynomials are continuous so we can evaluate"`
`"the limit by direct substitution"`

`rArrlim_(xto2)x^3+x+1`

`=2^3+2+1=11`

Answer 2

`3`

Explanation:

`"lim_(xto2)(x^3+1)/(x+1)`

`"this is not undefined nor indeterminate for x = 2"`
`"hence can be evaluated by direct substitution""`

`rArrlim_(xto2)(x^3+1)/(x+1)=9/3=3`
graph{(x^3+1)/(x+1) [-10, 10, -5, 5]}