Name:
College ID:
Thomas Edison State College
Calculus II (MAT-232)
Section no.: GS004
Semester and year: June 2006
Written Assignment 4
Answer all assigned exercises, and show all work. Each exercise is worth 10 points.
Section 6.6
2. Determine whether o
Name:
College ID:
Thomas Edison State College
Calculus II (MAT-232)
Section no.:
Semester and year:
Written Assignment 3
Answer all assigned exercises, and show all work. Each exercise is worth 10 points.
Section 6.4
2. Find the partial fractions decompos
Trigonometric Substitution
Whenever we have integrals involving expressions of the form
1 u2 , 1 u2 , u2 1
or variations, we can think about using trigonometric substitutions. For the first form, we
let u sin x. Then
1 u2 1 sin 2 x cos2 x.
For the second
Partial Fractions
From algebra we know that any polynomial with real coefficients can be factored as a
product of linear factors and irreducible quadratic factors. An irreducible quadratic factor
is one whose roots are complex numbers. If c is a root of p
Integration by Parts
Integration by parts is a method that substitutes one integral for another. The hope is that
the new integral will be integrable even though the original was not. The technique
consists of letting part of the integrand be designated b
Name:
College ID:
Thomas Edison State College
Calculus II (MAT-232)
Section no.:OL009
Semester and year: Dec 2016
Written Assignment 1
Answer all assigned exercises, and show all work. Each exercise is worth 5 points.
Section 5.2
2. Find the volume of the
Name: Justin Schneidt
Thomas Edison State College
Calculus II (MAT-232)
Section no.: GS003
Semester and year: November 2016
Written Assignment 2
Answer all assigned exercises, and show all work. Each exercise is worth 4 points.
Section 6.2
4. Evaluate the
Name: Justin Schneidt
Thomas Edison State College
Calculus II (MAT-232)
Section no.GS 003
Semester and year: November 2016
Written Assignment 4
Answer all assigned exercises, and show all work. Each exercise is worth 10 points.
Section 6.6
2. Determine wh
Name: Justin Schneidt
Thomas Edison State College
Calculus II (MAT-232)
Section no.:GS003
Semester and year: November 2016
Written Assignment 3
Answer all assigned exercises, and show all work. Each exercise is worth 10 points.
Section 6.4
2. Find the par
Name: Justin Schneidt
Thomas Edison State College
Calculus II (MAT-232)
Section no.: GS 003
Semester and year: Nov 2016
Written Assignment 5
Answer all assigned exercises, and show all work. Each exercise is worth 5 points.
Section 9.1
2. Sketch the plane
Name: Eleonor Lopez
College ID: 0515654
Thomas Edison State College
Calculus II (MAT-232)
Section no.:6.2, 6.3, 6.4, 6.6, 3.2
Semester and year: Jun 16
Written Assignment 2
Answer all assigned exercises, and show all work. Each exercise is worth 4 points.
Name: Eleonor Lopez
College ID: 0515654
Thomas Edison State College
Calculus II (MAT-232)
Section no.: 8.6-8.8
Semester and year: Jun 2016
section 8.6 solution
4. we have the series
k=0
let u k =
lim
k
k k
x
2k
| | |
k
u k+1
k k
k +1 k+1 2
x
then
by
Ra
The Shell Method
The shell method differs from the disc and washer methods most significantly in that the
strip taken is parallel to the axis and not perpendicular to it. The resulting differential
volume becomes a right circular cylinder with the inside
Polar Coordinates
In rectangular coordinates, for every ordered pair of real numbers (a,b) there is a unique
point in the coordinate plane. This is not true for polar coordinates. Let us first determine
how the point is located once the ordered pair (r,)
Arc Length
In applying the formulas for arc length, at first you may think that in many cases you
have an integral that is impossible to integrate. The best thing you can do is trust that
somehow the integrand can be simplified so that integration is poss
Power Series
With power series, to find the open interval of convergence, we always start by applying
the Limit Ratio Test. We use this limit to determine those values of x where the series
converges absolutely. Those values will always lie in an interval
Disk Method
In using the disk method, we take a strip of the enclosed region perpendicular to the axis
making sure that the entire strip lies in the region and that the same is true for any
arbitrary strip. If this is not the case, then we cannot use this
Taylor and Maclaurin Polynomials and Approximations
Just as we may consider the circle to be the limiting case of a polygon whose number of
sides tends to infinity, so may we consider a transcendental function to be the limiting
case of a polynomial whose
Sequences; Series and Convergence
Many of the results in chapter 8 of the textbook come from a theorem whose proof is
beyond the scope of this course. This theorem states that a monotonically increasing
sequence that is bounded from above converges; a mon
Taylor and Maclaurin Series
If we are given a function and we find its Maclaurin or Taylor series, then within its open
interval of convergence, the function and the series may be considered identical.
Furthermore, the series can be differentiated by term
Integral Test; Comparison of Series
As soon as we look at infinite series, we must not confuseas is easy to dothe nth
term of a series with the nth term of a sequence. If a series converges, its nth term must
tend to 0 as n . The converse, unfortunately,
Improper Integrals
In considering improper integrals, the first thing to do is to see where the integral is
improper. If one or both of the limits are or , then it is obvious. However, the
improper part of some improper integrals is hidden. For example,
z
Indeterminate Forms of LHpitals Rule
Using LHpitals Rule, we can show that there is a hierarchy of functions classified by
how quickly they tend toward infinity. For example, f ( x ) ln x tends to infinity more
slowly than f ( x ) x in the sense that
ln n
Alternating Series; Ratio and Root Tests
Until now we have been studying series of positive terms. We now look at the more
general situation. If we take the absolute value of each term in our series and we get a
convergent series, we say that the series c