Mathematics

Problem

Suppose that

\displaystyle \lim_{x\to 2} g(x)=4

. Which of the following additional conditions is sufficient to conclude that

\displaystyle \lim_{x\to 2} h\bigl(g(x)\bigr)=9

? a)

h

is differentiable at

u=4

. b)

h(4)=9

but no information is given about continuity. c)

h

is continuous at

u=4

and

h(4)=9

. d)

h

is continuous at

u=9

and

h(9)=4