Chapter Two: Limits Flashcards
1
Q
what is the basic trigonometric limit?
A
limx–>0 (sinx/x) = 1
2
Q
what is the limit as x approaches infinity of sinx/x?
A
limx–>∞ (sinx/x) = 0
3
Q
the extreme value theorem
A
if f is continuous on the closed interval [a, b], then f attains a minimum value and a maximum value somewhere in that interval
4
Q
the intermediate value theorem
A
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.
