Mathematics - 10 September 2007

Suppose the real valued f is unbounded in a neighborhood of a but its improper Riemann integrable exists anyway over the compact interval [a, b]. (A typical example is f(x) =1/sqrt(x) in [0,1], no matter the definition of f at 0). Let P_n be a sequence of partitions of [a, b] such that the norm of P_n (length of its largest interval) goes to 0 as n --> oo. Let S_n be a sequence of Riemann sums corresponding to P_n. Then, is it true that lim S_n = Integral a^b f(x) dx.

If f were bounded the answer would sure be yes, but since we have improper integrals I'm not sure.

Thank you for any help.

2007-09-10 04:58:48 · 2 answers · asked by Steiner 7

Using the Pythagorean Theorem calculate the value of x it the side measure b=^2 and c=25^2
a) 7
b) 13
c) 12
d) 4

2007-09-10 04:56:23 · 10 answers · asked by Anonymous

2007-09-10 04:51:32 · 5 answers · asked by James B 1

2007-09-10 04:50:27 · 4 answers · asked by Anonymous

2007-09-10 04:22:26 · 7 answers · asked by Anonymous

I know the formula is a^2+b^2=c^2 with a and b being legs and c being the hypotenuse. My question is why are the squares necessary? If everthing is squared, wouldn't that be the same as just a+b=c? I am so confused.

2007-09-10 04:05:09 · 11 answers · asked by Anonymous

I'm not asking for answers here, just how I set these up correctly to arrive at the answers. Thanks

1) x^3 = 15x^2 + 88x + 100 (3 solutions)

2) square root(x) + square root (x+1) = x (1 solution)

2007-09-10 03:57:17 · 4 answers · asked by Oztac 1

14 + 10x squared = 7y squared ...Please explain why or why not this is a function..and how you came up with the answer..thanks.

2007-09-10 03:51:03 · 5 answers · asked by ALF 2

f(x) =9xsquared - 8x -8 f(10)=
Please answer and explain step by step how to work this problem. I'm having MAJOR problems in my algebra class. Any websites that explain Domain and Functions would also be very helpful. Please explain how you came up with the answer.Thanks.

2007-09-10 03:47:56 · 5 answers · asked by ALF 2

can anyone figure this out?
In the absence of environmental constraints, population grows at a rate proportional to its size. Express the rate of population growth as a function of the size of the population.

2007-09-10 03:30:59 · 2 answers · asked by numbr1TXfan 4

1 kilometer equals how many mile? in what condition do we use mile?

2007-09-10 03:30:21 · 4 answers · asked by brian 2

2007-09-10 03:25:39 · 5 answers · asked by gssheng2000 1

2007-09-10 03:25:17 · 9 answers · asked by Dr D 7

Give a proof or a counterexample for each of the following statements: a. A – (B ∩ A) = A – B. b. A ⊕A = A.

2007-09-10 03:04:24 · 4 answers · asked by Carlos A 1

I've been thinking about this one problem for 2 days. The book does not give enough examples for me to figure it out. HEre is the problem.

A panel is being organized. You need to arrange a list of participants 4 administrators and 4 students. A) in how many ways can you list them if administrators must sit together in a group and students in a group? B) In how many ways can you list them if you must alternate students and administrators?

The answer on the back of the book says its 2*4!*4! = 1152. However it does not specified if this applies to part A) part B) or both. Plus I have no clue how they got this arrangement. Please provide how you came up with your answer. And yes its part of my homework but I just have no clue on how to solve this one.

2007-09-10 02:59:50 · 2 answers · asked by mr_gees100_peas 6

A) –32
B) –4
C) 4
D) 32

Please explain he answer.

2007-09-10 02:39:57 · 9 answers · asked by ray 1

1/64 - 4/9 = ?

2007-09-10 02:06:21 · 7 answers · asked by dragoi_stefan06 2

2007-09-10 01:59:58 · 7 answers · asked by kakalaky1 1

2007-09-10 01:53:15 · 5 answers · asked by Anonymous

Ok I am not looking for the answer I am just trying to figure out how to set up this problem so that I can find the answer so if you can please help I would greatly appreciate it!.......here is the problem.....a farmer wants to create a play space for his pet goats by enclosing a rectangle of land with a fence and then dividing it down the middle with another type of fence. the outer perimeter fence will cost $10 per foot and the fence across the rectangle (that divides the area into two parts) costs $5 per foot. find the dimensions of the rectangle that ives the largest amount of play space for $2006 worth of fencing, determine how much play space the farmer will have created

2007-09-10 01:45:14 · 2 answers · asked by Short and Sweet 2

2007-09-10 01:41:02 · 7 answers · asked by cecilia34581 2

1.) find the number of terms in the given Arithmethic Progression
-3,-11,-19,-27,.....,-115

2.)Three terms are in Arithmetic progression. If their sum is 21 and the sum of their squares is 149, what are the numbers?

3.) find S(sub)15 in Arithmethic progression 1,-7, -15,...,-111

hope you could help me with these...
I need your answers to verify my answers..I ll also try solving these...pls include ur solution!

that would be greatly appreciated!

2007-09-10 01:34:20 · 2 answers · asked by Anonymous

2007-09-10 01:31:14 · 13 answers · asked by kenneth j 1

2007-09-10 01:15:53 · 7 answers · asked by Anonymous

Can anyone give me situations/world problems involving linear functions and how to solve them?

2007-09-10 00:53:44 · 3 answers · asked by Anonymous

The plane kx - y + jz + 2 = 0 where k and j are constants intersect the point (2,0,3) and is parallell with the vector (1,-2,2). Determine the equation of the plane.

2007-09-10 00:43:07 · 3 answers · asked by Anonymous

1) x+y=-8
2) 2x-4y=8
your answers are very helpful I can not figure these out on a graph.

2007-09-10 00:34:31 · 7 answers · asked by sugar lady 1

Trisection of an angle

2007-09-10 00:26:10 · 5 answers · asked by Nipun M 1