# Find the Limit: $\lim_{x\to2^{+}}e^{3/2(2-x)}$

$$\lim_{x\to2^{+}}e^{3/2(2-x)}$$

Properties of the Natural Exponential Function:

The exponential function $f(x)=e^x$ is an increasing continuous function with domain $\mathbb R$ and range $(0, \infty)$. Thus $e^x>0$ for all $x$. Also

$\lim_{x\to-\infty}e^x$=0 and the $\lim_{x\to\infty}$ $e^x=\infty$

So the $x$-axis is a horizontal asymptote of $f(x)= e^x$.

How do I utilize this definition to solve this problem?

• What is $\lim_{x \to 2^+} 3/(2(2-x))$? – Kopper Jul 10 '15 at 15:14
• how must we read $3/2(2-x)$? don't you use $\LaTeX$? – Dr. Sonnhard Graubner Jul 10 '15 at 15:18

Since $$\lim_{x \to 2^{+}} \frac{3}{2(2-x)} = -\infty$$ then $$\lim_{x \to 2^{+}}\exp\left(\frac{3}{2(2-x)}\right) = \exp\left( \lim_{x \to 2^+} \frac{3}{2(2-x)}\right) = 0$$