Mathematics - 25 June 2007

Suppose f is differentiable on [0, oo) and lim (x --> oo) k f(x) + f'(x) = L, where L is finite and k >0. Then, prove that lim (x --> oo) f(x) = L/k and lim (x --> oo) f'(x) = o

2007-06-25 12:46:01 · 2 answers · asked by Tania 1

Prove the following theorem is true: “If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half its length.”

http://img.photobucket.com/albums/v225/warpedtrojan/05_08h_05a.gif

Given
R is the midpoint of OP
S is the midpoint of QP

Prove
RS is parallel to OQ
RS=.5(OQ)


Thanks!

2007-06-25 12:27:40 · 5 answers · asked by dastlyshs 1

1) I3x + 2I = - 8

2) I3x + 2I < - 8

3) I3x + 2I ≥ - 8


thank youu.

2007-06-25 12:11:07 · 6 answers · asked by jaz 5

In a company there are 100 employees, 50 men and 50 women. Out of the 50 men, 18 are fluent in French and don't know Math, 17 have a Phd in Math but don't speak French and 7 are fluent in French and have a Phd in Math.

Out of the women, 21 are fluent in French but don't know Math, 13 have a Phd in Math but don't speak French and 10 are fluent in French and have a Phd in Math.

The CEO wants to form a comission of 20 people, according to the following rules:

There must be 10 men and 10 women.
At least 8 people must be fluent in French
At least 9 people must have a Phd in Math.

How many comissions can the CEO form?

Thank you

2007-06-25 12:07:50 · 2 answers · asked by Tania 1

1. Some boy scouts helped traffic policemen. For every 3 policemen, there were 8 boy scouts. If there were 48 boy scouts how many traffic policemen were there?

2. Karl raises ducks for a living. He has 80 male ducks and 65 female ducks. If he sells 35 ducks what percent of all the duck will he sell?


Can you also explain how to get the answer?

2007-06-25 12:04:20 · 6 answers · asked by Tuesday 1

is -5>than square root of -5?

2007-06-25 12:02:24 · 10 answers · asked by Jake 1

On my homework, it says 'Solve each of the following by inspection.' Could you help me please?
Here's three of them:

1) I3x + 2I = - 8

2) I3x + 2I < - 8

3) I3x + 2I ≥ - 8

2007-06-25 11:56:49 · 1 answers · asked by jaz 5

2007-06-25 11:17:34 · 2 answers · asked by Anonymous

2007-06-25 11:06:26 · 9 answers · asked by Sarah P 1

(x+2)(x-3) = (x+3)^2

2007-06-25 11:05:48 · 7 answers · asked by Anonymous

F(x)=x-9 G(x)=root(x+7)

(F+G)(x)

How do i solve this?

2007-06-25 11:01:39 · 4 answers · asked by amshamah 3

into two lots by a fence parallel to the short side. If the area of the field is 25,000 ft^2, find the lengths of the sides so that the total length of the fence will be a minimum.


This is an optimization quesiton. Any ideas?

2007-06-25 10:50:48 · 4 answers · asked by Anonymous

pls i want someone who understands this concept very well to answer.

2007-06-25 10:17:00 · 10 answers · asked by missy prapjel 1

the "?" needed to be discovered to fit this expression

2007-06-25 10:16:34 · 2 answers · asked by Anonymous

Please give a star thank you.

2007-06-25 09:57:24 · 17 answers · asked by Anonymous

Help most welcome. Differentiate step by step:

1) arctan(2x)
2) e^(x^2+2)
3) arctan(2x)e^(x^2+2)

2007-06-25 09:46:21 · 3 answers · asked by Tp 2

4x + 1/2(12x -2) =3

2/3(x +8) =6x

2007-06-25 09:44:29 · 5 answers · asked by Jewman 1

2007-06-25 09:12:18 · 11 answers · asked by John D 2

Why is it that people that are math gurus cant convert there gifts into profits. Im sure some people will name a handfull of people who have, but 98,70956%:-) of math teachers, physicists and any other's that have these gifts barely make ends meat?

2007-06-25 09:11:03 · 5 answers · asked by Anonymous

How do you solve for X in this problem?

3x - 6 = 4x + 24

2007-06-25 09:09:25 · 14 answers · asked by Lindsay 3

lim x approaching 0 x / | x |

The back of the book states :

As x approaches 0 from the left, x / | x | approaches -1. As x approaches 0 from the right, x / | x | approaches 1. There is no single number L that the function values all get arbitrarily close to as x approaching 0.

I still don't understand this answer. Can someone clarify it for me? What is another way of answering this question? Can't we just state anything divided by zero is undefined?

2007-06-25 09:04:31 · 5 answers · asked by korr 2

[(y – x) / (x^2 *y)] + [(x + y) / (xy2)]

x2 + xy2
(2x2 + y2) / (x2y + 1)
( y2 + x2) / (x2y2)


thank you soo much for the help~~

2007-06-25 08:58:21 · 3 answers · asked by Anonymous

Please Help Me With This Trigonometry Question

How do I prove the following identity:

(COS beta / 1 - TAN beta) + (SIN beta / 1 - COT beta) = SIN beta + COS beta

If you could include the steps as to how to get the proof, I would greatly appreciate it, thanks!

2007-06-25 08:52:45 · 3 answers · asked by realpoeticyouth 1

Using exact values, verify that
Cos 60* = 1-2 Sin2 30*

With the work please

2007-06-25 08:51:02 · 4 answers · asked by . 2

2007-06-25 08:46:59 · 5 answers · asked by John D 2

how do you solve for x?

2007-06-25 08:35:38 · 1 answers · asked by swt16 1

How many marshmallows i can shove in my mouth at one time?

2007-06-25 08:35:14 · 9 answers · asked by Peter N 1

I'm wondering if anyone can help me with integrals and their applications. I just can't get the whole u substitution thing down. I know it undoes the chain rule but I don't know how to apply it. Also need help with derivatives and antiderivatives of exponentials and logarithmic functions. If anyone took some time to try and clear this stuff up for me I'd be eternally grateful.

2007-06-25 08:30:03 · 2 answers · asked by Big Thinker 3

I'm not sure of the reason why.

2007-06-25 08:24:52 · 7 answers · asked by bloodclate 1

2007-06-25 08:21:44 · 11 answers · asked by Michael H 3