Consider the rational function

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

p(x)=\dfrac{2x}{x-4}

. Which statement correctly characterizes the discontinuity of

p

x=4

? (a) Jump discontinuity, because

\displaystyle\lim_{x\to4^-}p(x)\neq\lim_{x\to4^+}p(x)

while both limits are finite. (b) Infinite discontinuity, because

p(x)

approaches

\pm\infty

x\to4

. (c) Removable discontinuity, because after applying L'Hospital's Rule one incorrectly finds

\displaystyle\lim_{x\to4}p(x)=2

. (d) No discontinuity; rational functions are continuous for all real

x