Analysis and Calculus

i need help when differiation of function in the form a^x. For example how to i work out the differiational of 2^x and 3^x?

how can i solve by Lebesgue integration ??????

hi...... Can anybody help me to get some exsample of Lebesgue integration

I have managed to work out some general solution for multiple angled trig equations which a number of people have checked and told me are good enough to publish as the work is completely orignal. How do I begin to get this work published and insure that the journal/magazine is at the right level for the work? Any ideas? Alex

Can anyone help me on this question,Using [math]\epsilon[/math]-[math]\delta[/math] definition of a limit to show that [math]\lim[/math] [math]\frac {2x^3-y^3}{x^2+y^2}[/math] = 0 (x,y)[math]\rightarrow[/math](0,0)

x2y2z=1 Find the points on the surface given above that are closest to the origin. z=x-2y-2 =>we just have to minimize D=x2+y2+(x-2y-2)2 I did this and got that all the critical numbers satisfy the equation x=y...doesn't seem right...can anyone verify or refute that?

guys i need help please ive been stuck on this problem for days: An object moving along a curve in the xy-plane has position (x(t), y(t)) at time t with dx/dt = cos(t^3) and dy/dt = 3sin(t^2) for 0<= t <= 3. At time t = 2, the object is at position (4,5). Find the position of the object at time t = 3. Please help! im stuck!

Hey. I can't understand why this is weird. I'm not familiar with the math notation so I'll explain it in words, it's not hard to explain. Take the derivative of ln(5 x^4). You get 4/x If you take the integral of 4/x, you get 4 ln |x| + C or ln (x^4) + C. But this is different than what the original function was, and that's what's confusing me.

I am having a problem here. I can't figure this out. [math]y=(3x-2)^4[/math] is [math]81x^4 - 216x^3 + 198x^2 - 96x + 16[/math]. The derivative for the above function is [math]y\prime = 12(3x-2)^3[/math]. The question is asking me to find out the pattern and write it is as an equation in the same form of the power rule. ([math]y=ax^n[/math] is [math]y\prime = anx^{n-1}[/math]). This goes same for [math]y=(2x^2 + 3)^5[/math] which is [math]y\prime = 20x(2x^2 + 3)^4[/math]. I got [math]y=(ax+p)^n[/math] and [math]y\prime = an(ax+p)^{n-1}[/math], which worked for the first function, but not the second. My teacher said that for the second function, "You k…

I am no genius, but I am sure Calculus shouldn't be so difficult for me to understand. I am having an awful time trying to grasp the main purpose for it. Through that I can figure it out myself....so I was hoping one of you people could take the time to explain it to me in plain basic english on how it works. I believe that everything should be able to be explained simply. I think my brain work on some sort of deductive method of seeing the whole picture, or tries to anyway, and then gets confused not know the basics and can't see the basics. SO. What I gather is that your trying to find the instanteous rate of change between "Something" as it reaches 0, or th…

What are the x values of all the critical points of this function?: f(x) = x³-6x²+12x-4 on the domain Df = [0, 5], as a set {in curly brackets} of the form: {a, b, ...} for real constants a, b, ...

Given f(x)=1/x; e(x)=x^2 + 4; g(x)=x^3 Consider g(e(f(x))), f(e(g(x))), and e(f(g(x))). Question: Make an intelligent conjecture about the relationship between the range of a composite function and the exponential powers of the original functions. g(e(f(x))) and e(f(g(x))) is [math]\frac{1}{x^6}+4[/math]. f(e(g(x))) is [math]\frac{1}{x^6+4}[/math]. The question is asking to find the relationship between the range of a composite function and the exponential powers of the original functions. For instance: g(e(f(x))), e(f(g(x))), and f(e(g(x))) have an infinity range. The exponentials of the original functions are: -1, 2, and 3. I'm not sure h…

In the equation: [math]\frac{d^2x}{dt^2} + K_1\frac{dx}{dt} + K_0x = 0[/math] Can someone please explain to me how I'm suppose to be able to use the trig answer [math]x=A\sin(rt + b)[/math] or [math]x=A\cos(rt + b)[/math] to get to the characteristic equation? Everytime I try to mush the equations around I get stuck at this junction: [math]-r^2x + K_1Ar\cos(rt + b) + K_0x = 0[/math] or [math]-r^2x - K_1Ar\sin(rt + b) + K_0x = 0[/math] I seriously need some help on this as I'm learning this stuff on my own, and therefore have no professor to turn to with questions.

after breaking down this fraction [math]\frac{x^2+2}{x^3-x}[/math] I got [math]\frac{-2}{x} + \frac{3}{2(x-1)} + \frac{1}{2(x+1)}[/math] but using my ti-89 and mathematic there is an extra +1 at the end so I was wondering where does the +1 come from? mathematic and ti-89 gave [math]\frac{-2}{x}+\frac{3}{2(x-1)}+\frac{1}{2(x+1)}+1[/math]

for example this problem http://www.geocities.com/coolageofempire/trig.JPG after solving it using trib substitution, my answer has square root inside the natural log but mathematica gives an answer same as mine without the square root so what is the problem here?

Who Can Name the Bigger Number? http://www.scottaaronson.com/writings/bignumbers.html this is a fun essay, written by Scott Aaronson when he was an undergraduate at Cornell. After some time at Berkeley, Princeton and the Inst. for Adv. Study, Scott is now at Waterloo University (same place as Lee Smolin, the quantum gravitist). He is an expert in computational complexity with interests in quantum computers and quantum information theory. And runs an occasionally entertaining blog http://www.scottaaronson.com/blog/ here e.g. is what he recently posted about the Turing Test for articfical intelligence http://www.scottaaronson.com/blog/2006/03/alan-turing-…

Help please! Two associative functions on the the unit square: [0,1]^2 -->[0,1] x,y --> T(x,y) and S(x,y) What is the ordinal sum of these two functions on [0,1]^2 ? I know it is not T(x,y)+S(x,y) Does ordinal some have something to do with ordinal numbers? Thanks

Ok, so I'm doing my computer science course with maths methods as a subject, which is a prerequisite to do this course, but I never done it in high school but somehow they accepted me (due to the fact I done another tertiary course in IT then went into Computer Science in university). So anyway, I figure they'll just revise the math methods formulas and such, and although I'll be a little behind, I'll be able to catch on quickly and wing the tests. So, heres the dilemma -not only are they not revising ANY math methods / specialist / calculas concepts, the lecturer is flowing through it like WATER! The people in my class have done 2 extra years of advanced maths in hig…

One of my professors tried to explain Cantor's Argument today. I'm not sure if he tried to do a dumbed down version or what, but it was kinda weird. He did this thing were we played a game. Player one had a 6x6 grid and player two got a row of 6 boxes. Player one then filled in each row of his grid with 0's and 1's in any order. For example: 000000 -row1 100000 -row2 110000 -row3 001100 -row4 011110 -row5 010101 -row6 and then it was player two's job to create a row of six that did not match any of player one's rows. The method was to take row 1 column 1 and put the opposite number in there. For my example that would mean player two puts a 1 in his first box…

Can someone show me how to graph a point in four dimensions? Particularly with cartesian coordinates. And then as a follow up, are there equivalents of spherical and cylindrical coordinates in 4-D? And there should be another new system or coordinates also, perhaps? Thanks.

Here I got a conceptual problem rarely mentioned by my teacher. When we try to figure the value of a definite integral, the general method is to find out the expression(value) of the indefinite integral, right? but, when we change the dx to d(-x), a must change must be produced correspondingly, that's changing the upper limit and lower limit, right? [math] \int_a^b x \,dx [/math]

1) let a1,b1>0 b_n+1=sqrt(a_n*b_n) a_n+1=(a_n+b_n)/2 prove the existence of lim an as n->inf and lim bn as n->inf, and prove that they are equal? i figure i need to use epsilon ofcourse but the problem is with N, what its quantity should be with regard to epsilon and the variables here. thanks in advance.

Your town has decided to drill a well to increase its water supply. As the town engineer, you have determined that a water tower will be necessary to provide the pressure needed for distribution, and you have designed the system shown below. The water is to be pumped from a 300-ft well through a vertical 4-in. pipe into the base of a cylindrical tank 20ft in diameter and 25 ft high. The base of the tank will be 60 ft above ground. The pump is a 3-hp pump, rated at 1650 ft*lb/sec. How long will it take to fill the tank the first time? (Include the time it takes to fill the pipe) (62.5 lb = 1 ft^3) I tried to do them separtely then add the work to fill the pip and ta…

For volume rotated, if two curves have more than 2 intersection pt., we must figure out in which region one is above the other, right? thanks

Greetings, I'm not likely to post again but I was having trouble with some maths and so I ran a search and found these forums in the hope somebody could answer my question. I understand this: " Given z = root(-9) (note: that's root of minus nine.) then z2 = (-9) .....................(1) (note: that's z squared) Let z = r cis o..................(2) (where o is phi) then z2 = r2 cis 2o Also, -9 = 9 cis p (where p is pi) equation (1) can be rewritten as: r2 cis 2o = 9 cis p r2 (cos 2o + isin 2o) = 9 (cos p+ isin p) hence, r2 = 9 equating the terms inside the brac…