\[ \lim_{x \to \infty} \left( 1 + \frac{1}{x + 8} \right)^x = e^{-9} \]
You asked:
Investigate the equation: \(\lim_{x \to \infty}{{\left( 1 + \frac{1}{x + 8} \right)}^{x}} = {e}^{-9}\).
MathBot Answer:
This equation has no unknown quantities, so it is either true or false.
This equation is false because the left-hand side is not equal to the right-hand side.
The left-hand side of the equation is:
\[\lim_{x \to \infty}{{\left( 1 + \frac{1}{x + 8} \right)}^{x}} = e\]The right-hand side of the equation is:
\[{e}^{-9} = e^{-9}\]\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).