A theorem about limits of functions often used in introductory analysis requires…
MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
A theorem about limits of functions often used in introductory analysis requires verification of three specific hypotheses involving a pair of comparison functions.
(a) List the three hypotheses that must be confirmed before the conclusion of the theorem can be drawn.
(b) Suppose h is a function satisfying x4≤h(x)≤3x4 for all x in an open interval containing 0, except possibly at x=0. Verify each hypothesis of the theorem for h with the comparison functions p(x)=x4 and q(x)=3x4.
(c) Applying your work in part (b), determine x→0limh(x) and justify your answer.