AP Calculus-Limits
Limits Involving Infinity
1.
What does
Name_
Date_ Period_
Explain in your own words the
meaning of each of the following.
3.
lim f ( x) L
x
lim f ( x)
tell you about the function
?
Explain in your own words the
meaning of each of the
AP Calculus
Review: Derivatives
1-6: Suppose the functions
Name_
D2-Day 8
and
f
g
and their
x
f '( x )
0
9
2
1
first
derivatives have the values given in the table to
the
right at
and
. Find the first derivative
x 1
x0
f ( x)
3
1
5
of each of the followin
AP Calculus
Name_Pd._
Motion
1. The height (in meters) of a projectile shot vertically upward from a point 2 meters
above ground level with an initial velocity of 24.5 m/s is
after t seconds.
h 2 24.5t 4.9t 2
a.) Find the velocity after 2 s and after 4s.
AP Calculus
Derivatives of Inverse
1-5: Find the derivative.
1.
2
y tan 1 ( x)
3.
y sin 1 (2 x 1)
5.
y x sin 1 x 1 x 2
Name_Pd._
2.
y tan 1 x 2
4.
G ( x) 1 x 2 arccos x
AP Calculus
Product & Quotient Rules
1-10: Differentiate
1.
f ( x ) ( x 2 2 x )e x
3.
5.
7.
H (u ) u u u u
t2 2
y 4
t 3t 2 1
9.
g (t )
t t
1
t3
2.
4.
1 2x
g ( x)
3 4x
Name_Pd._
(D1) Derivatives Day 4
g ( x ) xe x
x2 2
G ( x)
2x 1
6.
1
3
4 y 5 y 3
2
AP Calculus
Name_Pd._
Derivatives: Polynomials & Exponential Functions
1-21: Differentiate the Function
1.
2.
f ( x ) e5
4.
h( x) ( x 2)(2 x 3)
7.
5
3
y x x
10.
13.
16.
19.
2
3
4
3e x 3
x
k (r ) e r r e
g ( x ) x 2 (1 2 x )
y x8 12 x 5 4 x 4 6 x 5
2
f (t
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