Evaluate the following limits for the function :

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Evaluate the following limits for the function

y=\dfrac{1}{x}

: (i)

\displaystyle\lim_{x\to0^+}\frac{1}{x}

(ii)

\displaystyle\lim_{x\to0^-}\frac{1}{x}

(iii)

\displaystyle\lim_{x\to\infty}\frac{1}{x}

(iv)

\displaystyle\lim_{x\to-\infty}\frac{1}{x}

. Also state the quadrant in which the graph lies corresponding to each of the limits in parts (i) and (ii).