Consider the function h(x)= cases a x, & x 0, 1- x, & x>0

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

Problem

Consider the function

h(x)= \begin{cases} a\sin x, & x\le 0,\\ 1-\cos x, & x>0. \end{cases}

Which of the following statements about

a

guarantees that

h

is continuous at

x=0

? (a)

h

is continuous at

x=0

only if

a=0

. (b)

h

cannot be continuous at

x=0

for any real

a

. (c)

h

is continuous at

x=0

for every real value of

a

. (d)

h

is continuous at

x=0

only if

a=1