Homework Worksheet 10
1. Use Newtons Method to find the positive root of f ( x) x 3 7 x 7 , correct to 5
decimal places. Hint: Sketch a graph of this function first.
By examining the graph of f (x) ,
Homework Worksheet 11
2
1. Use the limit definition of the integral to evaluate
2
x x
0
2
2
dx .
3
2
n
n
2 0 2
2 2 i 2 2 2 lim 8 i 8 i 2 4
lim f 0
i lim
n
n n n i 1 n n 3 n n i 1 n 2
n3
3n
i
1
8
1. Farmer Brown wishes to erect a rectangular pen alongside his barn. The pen
will be divided into two smaller rectangular pens of equal area. The side common
to both pens will be perpendicular to the
Homework Worksheet 9
1. A farmer constructs identical adjoining rectangular pens, each with an area of 4500 square
feet. The fence for the outer boundary of the pens cost $3.00 per foot, while the fen
Homework Worksheet 7
dy
from the equation x 2 cos( y ) 2 y x
dx
2
x ( sin( y )dy cos( y )2 xdx 2dy dx
1. Compute
x 2 ( sin( y )dy 2dy cos( y ) 2 xdx dx
dy
dy
x 2 ( sin( y ) 2 cos( y )2 x 1
dx
dx
dy 2
1
has the following derivatives:
1 x2
2x
6 x2 2
f x)
(
and f ( x)
(1 x 2 ) 2
1 x2
Use calculus to find all local maxima and minima, if any, for the function.
1. The function f ( x) 1
Local maxima
Homework Worksheet 5- Section 3.4
1. Compute Dx
sin( x)
. Do not simplify your answer.
x2 1
( x 2 1) cos( x) sin( x)(2 x)
Quotient rule:
( x 2 1) 2
_
2. Find the slope of the tangent to the curve of f
Homework Worksheet 1
Name:_
Date:_
1. (2.4)Given the graph of f(x) at right, find:
a) f(2)
_does not exist_
b) lim f ( x)
x 2
_-9_
c) xlim1 f ( x)
_does not exist_
2. (2.4) Calculate the following lim
Homework Worksheet 4 Covering Sections 3.1, 3.2, and 3.3
1. Use the information given below
to draw the graph of the function
y f (x) near x=3.
f (3) 4
lim f ( x) 4
x 3
f 3) is undefined
(
Key: There
Homework Worksheet 6
1. A spherical ball has a radius of 3 inches. Use differentiables to approximate
the change in balls volume if the radius changes to 3.12 inches.
4
V r 3
3
dV
4r 2
dr
r 3.12 3 .1
Homework Worksheet 3
Name:_
sin x cos 2 x
1. (2.7) lim
x 0
3x
Date:_
sin x cos 2 x
sin x
cos 2 x
cos 0 1
lim
lim
1
x 0
x 0
3x
x x 0 3
3
3
lim
_1/3_
sin( 2 x )
t 0
3x
sin( 2 x )
2 sin( 2 x)
2 sin( 2 x
Homework Worksheet 2
Name:_
Date:_
1. (2.5) Write the precise , definition for the given limit: lim f ( x) N
x a
For every 0 , there exists a 0 such that if | x a | then | f ( x) N |
_
x 2 x 2
x 1 x 2
1. The graph of g(x) is shown:
a. (4 points) List all x-values on the interval (-10,10)
where the function is not continuous
_ -4, 2_
b. (6 points) List all x-values on the interval (-10,10)
where the
Quiz 4
Name:_
Date:_
Please circle your final solution:
1. A spherical balloon has a radius of 9 inches. Use differentiables to approximate the
change in the balls volume if the radius decreases to 8.
Quiz 3
Name:_
Date:_
3
(x
1. Using the limit definition of the derivative, calculate f ) when f ( x)
2x
3
3
3x 3( x h)
3h
f ( x h) f ( x)
3
2( x h) 2 x
2( x h) x
2 x( x h)
f x) lim
(
lim
lim
lim
lim
1. A rectangular sheet of metal is to be used to construct a box by removing a square from each
corner of the sheet of metal. Before the squares are removed, the sheet of metal is 3 feet wide and 8
fe
1. Evaluate the following definite integrals:
b
a.
3 sin
2
x cos xdx
0
_
4
b.
3 3
sin b _
3
x 2 x 3 dx
1
_ 793 / 6 _
3
c.
2
x x
4x
0
3
6 x 2
dx
_ 3 2 / 2 _
2. Evaluate the following indefinite integ
Homework Set 12
1. Let A(t) denote the area under the curve of y cos 2 x 2 and above the interval [0,t].
Find A
t
t
d
cos
(
cos 2 2
So, A(t ) ( x ) . Therefore A t ) ( x ) . By the first fundamental
Quiz 1
1. (2.4)Given the graph of g(x) at right,
find the following limits or clearly state
why they do not exist:
a. xlim8 g ( x)
-4
lim
b. x 0 g ( x)
Does not exist since the limit from the
left doe