Let $\displaystyle f(x) = |x|^{-1/2}$ for $\displaystyle x\neq0$. I need to show that $\displaystyle \lim_{x\to0+} f(x)= \lim_{x\to0-} f(x)=+\infty$...
Let $\displaystyle f(x) = |x|^{-1/2}$ for $\displaystyle x\neq0$. I need to show that $\displaystyle \lim_{x\to0+} f(x)= \lim_{x\to0-} f(x)=+\infty$...
To prove that:
$\displaystyle lim_{x\to 0^+} f(x) =+\infty$ you must prove that:
Because making the substitution y= -x in $\displaystyle \lim_{x\to -\infty} |x|^{-1/2}$ gives $\displaystyle \lim_{y\to\infty} |-y|^{-1/2}= \lim_{y\to\infty} |y|^{-1/2}$ which is, of course, the same as $\displaystyle \lim_{x\to \infty}|x|^{-1/2}$