Question

find the lim (x+1/x) as x tends to 0.and sketch a graph to support for answer.

Answer 1

\[lim_{x \rightarrow 0}(x+\frac{1}{x})=lim_{x \rightarrow 0}(\frac{x^2+1}{x})\]
From here you can see that the function gets larger and larger as x approaches 0 from the left and the right.
also, if you look at \[lim_{x \rightarrow \infty}(\frac{x^2+1}{x})=2\] \[lim_{x \rightarrow -\infty}(\frac{x^2+1}{x})=2\]from l'Hopital's rule