Question

How do you evaluate the limit `(x+3)^1997` as x approaches `-4`?

Answer 1

-1

Explanation:

If x approaches -4

`lim_(x->-4)(x+3)^1997=(-1)^1997`

Even numbers:
`(-1)^(2n)=((-1)^2)^n=1^n=1`
with n being an Element of `NN`

Uneven numbers:
`(-1)^(2n+1)=(-1)^(2n) * (-1)^1=1*(-1)=-1`
with n being an Element of `NN`

`1997=998*2+1`
`(-1)^1997=-1`