Evaluating Limits Graphically
Evaluating Limits Algebraically
Evaluating Limits to Infinity
100
(a)
(b)
(c)
(d)
a)3
b)DNE
c)DNE
d)3
100
Find the limit.
lim (2x2 + 3x + 3)
x→−3
What is 12?
100
lim x→∞ (5 + 8/x)
What is 5?
200
A)lim x→π/2 4 tan x
DNE
200
Find the limit of the trigonometric function.
lim cos
πx/3
x→8
What is -1/2?
200
lim x → ∞ (
(x^2-4))/(4x-2)
What is 1/4?
300
f(x)=1/2[[x]] + x – 3
Discuss the continuity of the function.
f is discontinuous at every integer.
300
lim (x2 − 9/x + 3)
x→−3
Write a simpler function that agrees with the given function at all but one point. Use a graphing utility to confirm your result.
g(x) =_____
What is (x-3)?
300
lim x→∞ (x+1)/(x^2+1)^1/3
What is infinity?
400
(a)lim x→5− f(x)
(b)lim x→5+ f(x)
(a) ∞
(b) ∞
400
Find the limit. (If an answer does not exist, enter DNE.)
lim (x + Δx)2 − 9(x + Δx) + 9 − (x2 − 9x + 9)/Δx
Δx→0
What is 2x-9?
400
lim x→-∞ (x + (x^2+3)
What is 0?
500
f(x) = tan πx4
a)lim x→6− tan πx4
b)lim x→6+ tan πx4
(a) ∞
(b) -∞
500
Find the limit of the trigonometric function. (If an answer does not exist, enter DNE.)
lim (cos(7θ) tan(7θ))/θ
θ→0
What is 7?
500
lim x→−∞ (3x+
(9x^2-x))
What is 1/6?