Ch. 2 Limits

Question 1

Definition: f(x) is continuous at x=a if…

Answer 1

f(a) exists
lim(x–>a)f(x) exists
lim(x–>a)f(x) = f(a)

Question 2

State the pinching theorem

Answer 2

if g(x) ≤ f(x) ≤ h(x) for all x ≠ a in some open interval containing a and lim(x–>a)g(x) = lim(x–>a)h(x) = L then lim(x–>a)f(x) = L

Question 3

Important trigonometric limits

Answer 3

lim(x–>0) sinx / x = 1

lim(x–>0) (1-cosx) / x = 0

Question 4

State the intermediate value theorem

Answer 4

if f(x) is continuous on [a,b] and u is any number between f(a) and f(b) then there exists at least 1 c in (a,b) s.t f(c) = u