Mathematics

Mathematics

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

.

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