Classwork Activity #7 Solutions MAT 254 Calculus I
18.) For f x x 2 , sketch the graph of f x and use this sketch to graph a sketch of
f x
20.) For f x x x 1 , sketch the graph of f x and use this ske
Calculus I MAT 254
Section 4.6 Related Rates
Example 1:
Hot air is pumped into a spherical balloon at a rate of 1000 ft3/min.
How fast is the radius of the balloon changing when the diameter is 50 ft?
Maria Pena
Citizen Kane
Before I start to watch Citizen Kane my thoughts was why we have to see this old
film is from 1941 and we are in 2015 the movies is 74 years old it doesnt make
no sense . I am
Classwork Activity #13 MAT 254 Calculus I
1.) Give the motion equation for an object thrown up with an initial velocity of
25 m
from the top of a building 100 m tall. Determine the elapsed time at whi
Classwork Activity #14 Solutions MAT 254 Calculus I
1.) A rectangle is inscribed with its base on the x-axis and its upper corners on the
parabola
y 5 x 2 . What are the dimensions of such a rectangle
Classwork Activity #14 MAT 254 Calculus I
1.) A rectangle is inscribed with its base on the x-axis and its upper corners on the
parabola y 5 x 2 . What dimensions of such a rectangle will give the gre
Classwork Activity #15 Solutions MAT 254 Calculus I
Example 1.)
Let A be the area of a circle with radius r. If
dr
dA
4 , find
when r 3 .
dt
dt
dA
dr
2 r
dt
dt
dr
dA
So when
4 and r 3 ,
2 (3)(4) 2
Classwork Activity #15 MAT 254 Calculus I
1.) Let A be the area of a circle with radius r. If
dr
dA
4 , find
when r 3 .
dt
dt
2.) A spherical snowball is melting in such a way that its diameter is de
Classwork Activity #16 Solutions MAT 254 Calculus I
1.) Estimate
21
1 x 2 dx using five left rectangles, five midpoint rectangles and five right rectangles.
Five left rectangles:
Five midpoint rectang
Classwork Activity #16 MAT 254 Calculus I
1.) Estimate
2
1
1
dx using five left rectangles, five midpoint rectangles and five right rectangles.
x2
2.) Given the graph of the function f ( x) below, est
Classwork Activity #13 Solutions MAT 254 Calculus I
1.) Give the motion equation for an object thrown up with an initial velocity of
25 m
from the top of a building 100 m tall. Determine the elapsed t
Classwork Activity #12 MAT 254 Calculus I
Differentiate the following composite functions h( x) f ( g ( x) using the chain rule:
Remember that h( x) f ( g ( x) g ( x) You may also need to apply the pr
Classwork Activity #12 Solutions MAT 254 Calculus I
Differentiate the following composite functions h( x) f ( g ( x ) using the chain rule:
Remember that h( x) f ( g ( x ) g ( x ) You may also need to
Classwork Activity #11 MAT 254 Calculus I
Part 1:
Find the derivatives of the following:
h( x ) e5 x
h(t ) (t 3 8t 1)8
h( x ) x 2 2 x
h( x) ln 5 x 2
h(t ) (t 3 ln t ) 2
h( s )
s
3
s 2s
2
Part 2:
Fin
ClassworkActivity#11SolutionsMAT254CalculusI
Part 1:
Find the derivatives of the following using the chain rule:
h( x ) e5 x
h(t ) (t 3 8t 1)8
h( x ) x 2 2 x
h( x) ln 5 x 2
h(t ) (t 3 ln t ) 2
s
h( s
Classwork Activity #10 MAT 254 Calculus I
Part 1:
Find the derivative of the following functions:
f ( x) e 2 x3
ex
x
f ( x) e 2 x
f ( x)
f ( x) x 2 e x
f ( x) (3 x 3 4)( x 5 7 x 2 1)
f ( x)
x2 2 x 1
Classwork Activity #10 Solutions
MAT 254 Calculus I
Part 1:
Find the derivative of the following functions:
f ( x) e 2 x 3 f x e 2 3 x 2 3e 2 x 2
f x xe e
ex
x
x2
f ( x ) e 2 x f x e x e x e x e x 2e
Classwork Activity #9 MAT 254 Calculus I
For the function f(x) = x4 5x2 + 4, find the derivative function f '(x), then determine the
equation of the line tangent to f(x) at x 1 and x 1 . Then find the
Classwork Activity #9 Solutions MAT 254 Calculus I
For the function f(x) = x4 5x2 + 4, find the derivative function f '(x), then determine the
equation of the line tangent to f(x) at x 1 and x 1 . The
Classwork Activity #8 MAT 254 Calculus I
The graph below is the derivative f x of a function f x . Assuming that f(0) = 0,
sketch a possible graph for f x .
The graph below is the derivative f x of a
Classwork Activity #17 Solutions MAT 254 Calculus I
Find
3
2
2 x 1 dx using the Evaluation Theorem.
Solution: First find an antiderivative of f x 2 x 1 This would be F x x 2 x
Then find F 3 F 2
x
2
Classwork Activity #17 MAT 254 Calculus I
1. Find
3
2
2 x 1 dx using the Evaluation Theorem. Check your answer with your
calculator.
2. Find
6
3. Find
5
4. Find
1
t 2 dt using the Evaluation Theorem.
Dems look to health vote without abortion
foes
Play Video ABC News Health Care: Getting House Members
On Board
Slideshow:Health Care
Play Video Video:Thousands march for health care reform WCNC Charlo
The GOP's Dirty Health-Care Secret
by Matthew Dallek
Matthew Dallek teaches history and politics at the University of Californias Washington Center.
He is the author of The Right Moment: Ronald Reagan
`Avatar' rules with $68.3M, tops $1B
worldwide (AP)
Source: AP Sun Jan 03, 2010, 2:08 pm EST
LOS ANGELES - James Cameron's science-fiction epic "Avatar" had another stellar weekend
with $68.3 million
Hillary Rodham Clinton is taking bold
approach with new strategy
By Bill Barrow
Associated Press
Friday, July 24, 2015
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