Consider . Which of the following is sufficient to guarantee that is continuous at…

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

Problem

Consider

p(x)=\sin x+\ln(1+x)

. Which of the following is sufficient to guarantee that

p

is continuous at

x=0

? (a)

p(0)

exists and equals

0

, so

p

is continuous at

x=0

. (b)

p'(x)

exists for

x

near

0

, which guarantees continuity at

x=0

. (c) Both

\sin x

and

\ln(1+x)

are continuous at

x=0

, therefore their sum

p

is also continuous there. (d)

\ln(1+x)

is defined at

x=0

and

\sin x

is bounded near

0

, so their sum must be continuous at

x=0