# Question 61e49

Jan 21, 2018

${e}^{x} > 0$ , $x$$\in$$\mathbb{R}$

#### Explanation:

Impossible. ${e}^{x}$ has no solutions.

${e}^{x} > 0$ for each $x$$\in$$\mathbb{R}$

Graph of ${e}^{\frac{1}{x} ^ 2}$

Jan 21, 2018

There is no solution.

#### Explanation:

${e}^{\frac{1}{x} ^ 2} = 0$

$\to \frac{1}{x} ^ 2 = \ln \left(0\right)$

-> x = sqrt(ln(0)#

Of course you run into the problem of: $\ln \left(0\right)$ which does not have a value (it is undefined). So in effect, we will not find a value of $x$.

If you plot the graph of the function: graph{e^(1/x^2) [-9.58, 9.78, -2.59, 7.09]}

we can see the function asymptotically approaches $1$. More to the point it never crosses $y = 0$ so there does not exist any value of $x$ for which the equation is satisfied.