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 sketch to graph a sketch
of f x
21.) For f x cos x , sket
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?
If the balloon's volume increases at a constant rate,
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 not going to like because is going to be black and whit
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 which it
sec
will hit the ground, its final velocity, and
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 that will give the greatest
possible area?
Area 2 x(5
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 greatest possible
area?
2.) A Norman window has the shape
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) 24
dt
dt
A r2
Example 2.)
A spherical snowball is melti
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 decreasing at rate of
0.2 cm/min. At what rate is the vol
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 rectangles:
Five right rectangles:
2.) Given the graph below:
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, estimate the area under the graph of f
from x = 0 to x = 1
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 time at which it
sec
will hit the ground, its final velo
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 product rule or
the quotient rule.
h( x) esin x
h( x) sin
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 apply the product rule or
the quotient rule.
h( x) esi
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:
Find the equation of the tangent line to h( x)
8
4 3x
8
(
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 )
32
s 2s
Solutions:
h( x) 5e5 x
h(t ) 8 t 3 8t 1 3t
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
x 1
Part 2:
From the table below calculate the quantit
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 2 x
x
x
f ( x)
f ( x) x 2 e x f x 2 xe x x 2 e x
f ( x
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 point a4t which
these two tangents intersect.
The grap
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 . Then find the point a4t which
these two tangents intersect
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 function f x . Assuming that f(0) = 0,
sketch a possibl
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
x
Find
6
1
3
2
32 3 2 2 6 4 (2) 6 6 0
2
t 2 dt using t
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. Check your answer with your calculator.
2
1
dx using th
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 Charlotte
Related Quotes
Symbol Price Change
^DJI 10,611.84 +
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's First Victory and the Decisive Turning
Point in Amer
`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 domestically, shooting past $1 billion worldwide, only
Hillary Rodham Clinton is taking bold
approach with new strategy
By Bill Barrow
Associated Press
Friday, July 24, 2015
Comments (1)
Share on email
Share on print
More Sharing Services
Share on twitter
Follow News
GREENVILLE, S.C. In her second bid for th
User Reviews
The film equivalent of a straight A student getting a B2 May 2015 | by hunter logan (United States) See all my reviews
Superhero movies, blockbusters, and the world received something special from The Avengers,
which expertly blended cinemati
10 Things Movie Theaters Won't Tell You
by Sarah Morgan
Thursday, December 31, 2009provided by
1. "We're obsolete? No way!"
Hard to believe, but movie theaters have been holding their own, despite intense competition
from cable, the Internet and other med
Human Evolution Project
Luke DeMio
Australopithecus;
Appearance: The face has a characteristic dished appearance. Male australopithecines were
larger in body size. Males were taller and heavier than Females. They looked like an ape and
were 3-1/2 feet tal
User Reviews
If you listen very closely you can hear the sound of the superhero bubble bursting.
23 April 2015 | by white_water See all my reviews
I'll say this: If you don't mind more of the same you'll probably love this movie. If you wanted
something d
Matthew DeMio
Mrs. Parenti
English 9A C
13 September 2010
Favorite Book Essay
My favorite book, as of this time, is undoubtedly the Hitchhikers Guide to the Galaxy, by
Douglas Adams. It focuses on the plot of an extraordinarily average man, named Arthur D