A function is described as follows: • For , (a horizontal line)

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

Problem

A function

q

is described as follows: • For

x\le -1

q(x)=2

(a horizontal line). • For

-1<x<1

q(x)=\sqrt{1-x^{2}}

(the upper half of a circle of radius

1

centered at the origin). • For

x\ge 1

q(x)=x-1

(a line of slope

1

). Which of the following statements is true? (a)

\displaystyle \lim_{x\to -1} q(x)=0,\text{ and } q \text{ is continuous at } x=1.

(b)

\displaystyle \lim_{x\to -1} q(x)\text{ does not exist, and } q \text{ is continuous at } x=1.

(c)

\displaystyle \lim_{x\to -1} q(x)\text{ does not exist, and } q \text{ is discontinuous at } x=1.

(d)

\displaystyle \lim_{x\to -1} q(x)=2,\text{ and } q \text{ is discontinuous at } x=1.