Mathematics

Problem

Let

q(x)=x^{4}+2x^{2}+1

. Answer the following questions. a. (i) Prove that

q(x)

is continuous at every real number. b. (ii) Using the result of part (i), establish that

\displaystyle \lim_{x\to c} q(x)=q(c)

for an arbitrary real number

c

. c. (iii) Verify the statement of part (ii) explicitly for

c=-1

by direct calculation of the limit.