Answer
$\lim\limits_{t \to 0}\dfrac{e^{5t}-1}{t}$
We could guess that the value of the limit is $5.0$.
Work Step by Step
$\lim\limits_{t \to 0}\frac{e^{5t}-1}{t}$
We can evaluate the function at the given numbers:
$t = 0.5$:
$\frac{e^{5(0.5)}~-1}{0.5} = 22.364988$
$t = -0.5$:
$\frac{e^{5(-0.5)}~-1}{-0.5} = 1.835830$
$t = 0.1$:
$\frac{e^{5(0.1)}~-1}{0.1} = 6.487213$
$t = -0.1$:
$\frac{e^{5(-0.1)}~-1}{-0.1} = 3.934693$
$t = 0.01$:
$\frac{e^{5(0.01)}~-1}{0.01} = 5.127110$
$t = -0.01$:
$\frac{e^{5(-0.01)}~-1}{-0.01} = 4.877058$
$t = 0.001$:
$\frac{e^{5(0.001)}~-1}{0.001} = 5.012521$
$t = -0.001$:
$\frac{e^{5(-0.001)}~-1}{-0.001} = 4.987521$
$t = 0.0001$:
$\frac{e^{5(0.0001)}~-1}{0.0001} = 5.001250$
$t = -0.0001$:
$\frac{e^{5(-0.0001)}~-1}{-0.0001} = 4.998750$
We could guess that the value of the limit is $5.0$
