, h(x)= cases f(x), & x 2 . cases Then which of the following does not…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

f(x) = \frac{2 \cos x - \sin 2x}{x - 2x^2}

g(x) = \frac{e^{\cos x} - 1}{8x - 4\pi}

h(x)= \begin{cases} f(x), & x < \frac{\pi}{2},\\ g(x), & x > \frac{\pi}{2}. \end{cases}

Then which of the following does not hold? (1)

h

is continuous at

x = \pi/2

(2)

h

has an irremovable discontinuity at

x = \pi/2

(3)

h

has a removable discontinuity at

x = \pi/2

(4)

f\left(\frac{\pi}{2}\right) = g\left(\frac{\pi}{2}\right)