Fundamentals of Calculus
Name
Integration I
Find the integral for each of the following:
3
1. (2 x 4)dx =
0
3
2. (2 x 7) 2 dx =
1
5
3. (2 x 3 5 x 2 9 x + 2)dx =
2
4.
(2 x 4 5 x 3 + 7 x 2 )
dx =
2x
3
1
5
5. ( x 7) 2 dx =
1
4
6. ( 5 x 2 x + 7)dx =
2
9
9. (3
Fundamentals of Calculus
Implicit Differentiation II
Find
dy
for each of the following:
dx
1. 3 y 2 = sin x
2. tan(2 x y ) = 3 x 2
3. 3 y 2 = 2 x + y
4. sin 3 y = 3x 5 2 y 3
5. Write equation of tangent line at the point (6, 2) for
2x
= 3.
y2
Fundamentals of Calculus
Worksheet on Implicit Differentiation I
Find
Name_
dy
for each of the following, circle your answer:
dx
1. x 2 + y 3 = 9
2. 5 y 2 = sin( x)
3. sin(3 y ) = 5 x 2
4. 2 x = sin(3 y )
5. x 3 + 3 xy 2 = 5 x
6. tan( x + y ) = 9
2x2 5
7.
Fundamentals of Calculus
Name
Worksheet III - Derivative of the Exponential and Logarithmic Function
Notes:
dx
d
1
(e ) = e x
(ln x) =
dx
dx
x
du
d
u'
(e ) = e u * u '
(ln u ) =
dx
dx
u
1. y = e 2 x
2. y = e7 sin 3 x
3. y = e8sin
4. y = 7 x ln( x + 2)
5.
Fundamentals of Calculus
Name
Worksheet II - Derivative of the Exponential and Logarithmic Function
Notes:
dx
d
1
(e ) = e x
(ln x) =
dx
dx
x
du
d
u'
(e ) = e u * u '
(ln u ) =
dx
dx
u
2. y = e7 x sin x
3. y = e3cos
4. y = 3x ln( x + 2)
5. y = 8ln(2 x3 5
Fundamentals of Calculus
Name
Worksheet I Derivative of the Exponential and Logarithmic Function
Notes:
dx
(e ) = e x
dx
du
(e ) = e u * u '
dx
d
1
(ln x) =
dx
x
d
u'
(ln u ) =
dx
u
1. y = e 2 x
2. y = esin x
3. y = e3cos7 x
4. y = ln( x + 2)
5. y = 8 ln(
Fundamentals of Calculus
Worksheet III
Find the derivative of each of the following:
1. y = sin 3 5 x
2. y = tan 5 (3 x 5)
3. y = 2 x sin 4 3 x
4. y = 4 csc5 (3 x)
5. y = 5 x sec5 (3 x)
6. y = 6 cot 2 (3x 8)
7. y = 2 tan(5 x 3)
8. y = 2 x 3 2sin(3 x 7)
9.
Fundamentals of Calculus
Name:_
Hill - Position, Velocity, Acceleration II
From a platform of 80 feet, a ball is thrown up into the air and then falls. The
height of the ball in feet over time, t seconds, is given by:
s (t ) = 16t 2 + 64t + 80
a) Find the
Fundamentals of Calculus
Velocity, Acceleration I
Name:_
When a particle moves in our world, gravity has an affect on its position. The
general equation for a particles path in 3 dimensions is given by:
s (t ) = 16t 2 + v0t + h0 , t 0. Time, t in seconds
Fundamentals of Calculus
Review Sheet derivatives, Vel, Acc.
I.
Find
dy
for each of the following:
dx
1. y 2 = sin 3 2 x + tan y
2. y = ln(3 x 2) 4
3. y = 2e 2 cos 4 x + 4 5 x
4. y =
5. ln y = ln 5 (3x 5) 2 (4 x + 1)3
6. 3 x 4 y 6 = sin(3x 2 y )
(3x 2)
5
Fundamentals of Calculus
Optimization-V
Name_
Notes:
1. One of the most common applications of calculus involves the
determination of minimum and maximum values. Just think how many
times you have said, What is .the greatest cost, least profit, maximum
pr
Fundamentals of Calculus
Optimization-IV
Name_
Notes:
1. One of the most common applications of calculus involves the
determination of minimum and maximum values. Just think how many
times you have said, What is .the greatest cost, least profit, maximum
p
Fundamentals of Calculus
Name
Integration III
Find the integral for each of the following:
2
1. (5 x + 4) dx =
1
4
2. (2 x 9) 2 dx =
1
3
3. (8 x 3 6 x 2 2 x + 1)dx =
1
4.
3
1
(2 x 3 5 x 2 + 9 x)
dx =
2x
4
5. ( x + 1) 2 dx =
1
32
6. ( 5 x + 6 x 7)dx =
1
16
Fundamentals of Calculus
Name
Integration II
Find the integral for each of the following:
3
1. (2 x + 4)dx =
0
3
2. (3 x + 7) 2 dx =
0
4
3. (4 x 3 6 x 2 8 x + 2)dx =
2
4.
3
1
(2 x 3 5 x 2 + 9 x)
dx =
2x
9
5. ( x + 5) 2 dx =
1
32
6. ( 5 x 2 x + 7)dx =
1
9