Chapter Two: Limits

Question 1

what is the basic trigonometric limit?

Answer 1

lim_x–>0 (sinx/x) = 1

Question 2

what is the limit as x approaches infinity of sinx/x?

Answer 2

lim_x–>∞ (sinx/x) = 0

Question 3

the extreme value theorem

Answer 3

if f is continuous on the closed interval [a, b], then f attains a minimum value and a maximum value somewhere in that interval

Question 4

the intermediate value theorem

Answer 4

if f is continuous on the closed interval [a, b], and M is a number such that f(a) ≤ M ≤ f(b), then there is at least one number c in the interval [a, b] such that f(c) = M.

If f is continuous on the closed interval [a, b] and f(a) and f(b) have opposite signs, then f has a zero in that interval.