Answer
1
Work Step by Step
We have to compute $\lim\limits_{x \to 0} \left(\dfrac{1}{x}\right)^x$.
We use a calculator to evaluate the function $f(x)=\left(\dfrac{1}{x}\right)^x$ for values of $x$ very close to 0.
Let $x_1=0.000001,x_2=0.0000001, x_3=0.00000001$.
$f(x_1)=f(0.000001)=\left(\dfrac{1}{0.000001}\right)^{0.000001}=1.00001381561$
$f(x_2)=f(0.0000001)=\left(\dfrac{1}{0.0000001}\right)^{0.0000001}=1.00000161181$
$f(x_3)=f(0.00000001)=\left(\dfrac{1}{0.00000001}\right)^{0.00000001}=1.00000018421$
Therefore we have:
$\lim\limits_{x \to 0} \left(\dfrac{1}{x}\right)^x=1$
