exponential function

The sum of the following infinite series is: $$ \frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+\frac{1}{5!}+\ldots $$

Let x be a continuous variable defined over the interval (-∞, ∞), and f (x) = e^-x - e^-x. The integral g(x) = ∫ f(x) dx is equal to

The Laplace transform $F(s)$ of the exponential function, $f(t)=e^{at}$ when $t\ge0$, where $a$ is a constant and $(s-a)>0$, is

Let $$x$$ be a continuous variable defined over the interval $$\left( { - \infty ,\infty } \right)$$, and $$f\left( x \right) = {e^{ - x - {e^{ - x}}}}.$$ The integral $$g\left( x...

The expression $$\mathop {Lim}\limits_{a \to 0} \,{{{x^a} - 1} \over a}\,\,$$ is equal to

The infinite series $$1 + x + {{{x^2}} \over {2!}} + {{{x^3}} \over {3!}} + {{{x^4}} \over {4!}} + ........$$ corresponds to

The function $$f\left( x \right) = {e^x}$$ is _________.

$${e^z}$$ is a periodic with a period of