Download AP CALCULUS TEST REVIEW 1.4-1.5 1. Use the graph to find lim f(x)

AP CALCULUS TEST REVIEW 1.4-1.5
lim f (x)
lim f (x)
x→ 4 +
x→−1+
1. Use the graph to find lim− f (x) .
2. Use the graph to find lim− f (x) .
x→ 4
x→−1
lim f (x)
lim f (x)
x→ 4
x→−1
10
10
9
9
8
8
7
7
6
5
Y Axis
Y Axis
6
4
5
4
3
3
2
2
1
0
1
0
1
2
3
4
5
6
7
8
9
10
0
-5
X Axis
-4
-3
-2
-1
0
1
2
3
X Axis
3-4. Use the graphs from #1-2 to identify values of x where the functions would be
discontinuous. Classify these discontinuities as removable or non-removable.
!
!
!
!
!
!
Find the value(s) of x (if any) for which the function is discontinuous and classify these
discontinuities as removable or nonremovable.
5.
7.
!
!
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f (x) =
x+2
x − 3x − 10
6. f (x) = cos
2
⎧−2x + 3,
f (x) = ⎨ 2
⎩x ,
x <1
x ≥1
πx
2
4
5
!
Find the limit of each of the following analytically, if possible. If the limit does not exist,
explain how you reached that conclusion.
!
x −1
2+x
lim+
lim+
8. x→1 x − 1
9. x→1 1 − x
πx
. Find each limit (if it exists).
4
lim f (x)
lim f (x)
a) x→−2+
b) x→−2−
10. Let f (x) = sec
⎧−2x,
11. Let f (x) = ⎨ 2
⎩ x − 4x + 1,
lim f (x)
a) x→2+
x≤2
x>2
c) lim f (x)
x→2
. Find each limit (if it exists).
b)
lim f (x)
x→2 −
c) lim f (x)
x→2
!
12. Find all vertical asymptotes of f (x) =
1
.
sin(2x)
13. Find all vertical asymptotes of f (x) =
x3 + 1
.
x +1
14. Verify that the Intermediate Value Theorem applies to the indicated interval and the
value of c guaranteed by the theorem.
f (x) = x 2 + x − 1,
[0, 5], f (c) = 11
Know the intermediate value theorem and how it applies to continuity.
Also be able to graph a function with given characteristics !
(vertical asymptotes, discontinuities, etc.)