Mathematics

Problem

Evaluate the limit of the composite polynomial expression and comment on continuity at the indicated point. a. (i) Calculate

\displaystyle \lim_{x\to 2}(3x^{2}+5)^{4}

. b. (ii) Find the left–hand limit and the right–hand limit of the same expression as

x

approaches

2

. c. (iii) State, with reason, whether the function

g(x)=(3x^{2}+5)^{4}

is continuous at

x=2