Mathematics

Problem

Consider the following statements for the function

y=\dfrac{1}{x}

. (I)

\displaystyle\lim_{x\to0^+}\dfrac{1}{x}=+\infty

(II)

\displaystyle\lim_{x\to0^-}\dfrac{1}{x}=+\infty

(III)

\displaystyle\lim_{x\to-\infty}\dfrac{1}{x}=0^{-}

(IV)

\displaystyle\lim_{x\to+\infty}\dfrac{1}{x}=0^{+}

Which option below lists all the true statements? a) (I) and (IV) only b) (I), (III) and (IV) only c) (I), (II) and (IV) only d) (I) and (III) only