Answer
The number $e$ is defined as: $\lim\limits_{h \to 0} \frac{e^h - 1}{h}=1$.
$\lim\limits_{h \to 0}\frac{2.7^{h}-1}{h} = 0.99$
$\lim\limits_{h \to 0}\frac{2.8^{h}-1}{h} = 1.03$
The value of $e$ is between 2.7 and 2.8.
Work Step by Step
The number $e$ is defined as: $\lim\limits_{h \to 0} \frac{e^h - 1}{h}=1$.
$\lim\limits_{h \to 0}\frac{2.7^{h}-1}{h} = 0.99$
$\lim\limits_{h \to 0}\frac{2.8^{h}-1}{h} = 1.03$
You can find these values by using the table feature on a graphing calculator and finding values that are close to zero.
The value of $e$ is between 2.7 and 2.8 since the above limits are around 1.
