Introduction to Limits
Calculus 12
name: _____________________
1. Give the meaning of the phrase “ the limit of f(x) as x a” in your own words.
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Write that phrase in limit notation:
2. Determine the following limits numerically (sketch a few values in a table of values)
a)
x−2
lim
2
x2 x − x − 2
b)
lim
x0
c)
lim
x0
x+3− 3
x
sin x
x
3. Use the graph of each function to determine the indicated limit.
y
If it Does Not Exist, explain why.
a)
lim tan x
x π
2
x
−π
−π/2
π/2
π
3π/2
y
b)
lim 4 − x
x0
x
y
c)
x
lim f ( x )
x2
y
d) lim
x1
x−5
x−5
x
e) lim
x0
cos
1
x
dne
y
x
−π
− π/ 2
π/ 2
π
3 π/ 2
4. Determine these limits using your calculator and either of the above methods
a)
lim( x + 3)
c)
lim(3 x )
x→2
x→0
b)
lim(3)
d)
lim( x 2 + 1)
x→6
x →1
5. a) Explain the meaning of the notation
lim f ( x ) = 25
x →8
b) does it mean that f(8) = 25 ?
6. Let’s say that f(2) = 4.
Does that mean that
lim f ( x ) = 4
?
Explain.
x→2
-------------------------------------------------------------------------------------------------------------------------2a)
1
1
b)
c) 1
3
2 3
3 a)d)e) DNE
5 & 6 will discuss in class tomorrow
b) 4 c) 2
4.
a) 5 b) 3 c) 0 d) 2