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

Mar 11, 2018

-1

#### Explanation:

If x approaches -4

${\lim}_{x \to - 4} {\left(x + 3\right)}^{1997} = {\left(- 1\right)}^{1997}$

Even numbers:
${\left(- 1\right)}^{2 n} = {\left({\left(- 1\right)}^{2}\right)}^{n} = {1}^{n} = 1$
with n being an Element of $\mathbb{N}$

Uneven numbers:
${\left(- 1\right)}^{2 n + 1} = {\left(- 1\right)}^{2 n} \cdot {\left(- 1\right)}^{1} = 1 \cdot \left(- 1\right) = - 1$
with n being an Element of $\mathbb{N}$

$1997 = 998 \cdot 2 + 1$
${\left(- 1\right)}^{1997} = - 1$