Analysis and Calculus

I have reason to think that if A, B and N in the following equation are positive whole numbers then there is no solution. I would like either values of A, B and N which satisfy the equation or a reason why there is no solution. If you think it looks easy then give it a go - please.

In solving an integral of sqrt(9-x2), we substitute x=3sin(t) to get an integral of 3cos(t). Why does this work? In the original function, x can take on any value(if you include imaginary numbers), but the new function is equivalent to the original one even though sin(t) takes values only between its amplitudes. P.S. I remember a guide to writing math in this forum. Anyone have the link?

Want to ask a moronic question, can anyone answer me!! 48÷2y =24y or 24/y?

1-Even number 2-Prime number 3-Not prime 4-Non of these Please explain yor answer

according to the source* , this expression f(m) is a fact one "notices" in order to get the value for m infinite ...... which is 26 ! * les math au carré , by Marie-France Palissard

Has there ever been a formal proof of the following formula? [math]\sum_{n=0}^\infty {1\over (7n+1)^2}+{1\over (7n+2)^2}-{1\over (7n+3)^2}+{1\over (7n+4)^2}-{1\over (7n+5)^2}-{1\over (7n+6)^2} \stackrel{?}{=}{24\over 7\sqrt{7}}\int_{\pi/3}^{\pi/2} \! \log {|{\tan{t}+\sqrt{7}\over \tan{t}-\sqrt{7}}|} \mathrm{d}t \approx 1.15192[/math] The most recent result I can find is from Bailey&Borwein (2005), who have shown that the identity holds to at least 20,000 decimal places. Yet, no proof that it is exact has been known at that time. The Bailey&Borwein (2005) paper can be found here: http://crd-legacy.lbl.gov/~dhbailey/dhbpapers/math-future.pdf Thanks, Da…

links deleted The most difficult math problem of all time - solved in a perfunctory, concise way, an accepted way, consistently; and without error. Exposition And Sub-Proofs of Landau's Pole Prime Number Theory; Group Coordinates Magnitude Theory The Rho Function - Measure of density of prime number (and then general exponential) distribution; in the reals. A prime number is a foundational unit of arithmetic distribution (multiplication), and thus comprises the building-block root of Categorical Set Theory. Prime numbers are arbitrarily and relatively dipolar. Upon set-theoretic recombination (or substitution), this proves Goldbach's Conjecture for any set …

Can someone put up a tutorial on Integral Calculus just like there is one for differentiation? I need it.

I want to know about the functions which is path independent and path dependent. Please describe me about this.

from a high school level math book "les math au carré" by M-P. Falissard , page 133 n integer she uses the expression to deduce the limit of the sum as m approaches infinity (26) my gratitude to any solid help on this one !

lim (x-x) for x going to infinity equals? Is it simply 1? r

Taylor stated that: The curve is subjunctive to a partial of an infinite number of its differentials. So, we must be dealing with limited mathematics. Correct!

can some one help me with question 15. i am integrating it and trying this 1/3 (9)^3 -(1/3 (1)^3) and this gives me a answer of 242.66667 but the answer at the back of the book is 17 2/3

In proving that :[latex]x\leq y\wedge 0\leq z\Longrightarrow xz\leq yz [/latex] we have the following proof: Let ,:[latex]x\leq y\wedge 0\leq z[/latex] and let ,[latex]\neg(xz\leq yz) [/latex].......................................................1 But from (1) and using the trichotomy law we have :yz<xz.And using the fact [latex]0\leq z[/latex] we have for 0= z, y0<x0 => 0<0 , a contradiction since ~(0<0) Hence [latex] xz\leq yz[/latex]

The physics group have redirected me here. All parameters are constant save the Delta t terms. Related but a bit more involved is The divisor is essentially a large positive value with a small 'wiggle', but it would be nice to have an analytic solution. Many thanks for your time. Seth

Please describe me about simply connected and multiply connected curve.

A cylinder with radius r=0.75 m and height h = 1 m has to be covered by a cone. Find the minimal area for the cone. Surface Area of Cone: pi*r^2 + pi*r*L So, I figured out: H= Height of the cone R= Radius of the cone (H-1)/0.75 = H/R H=-4R/(-4R+3) To calculate L, I used the Pythagoras & substituted H from above: L = sqrt(R^2+H^2) L = sqrt(R^2+(-4R/(-4R+3)) L = (sqrt(16R^4-24R^3+25R^2)/(4R-3) I see I'm heading towards something really complicated... Could you please help me find the right way to do it? I have just started doing this.

For finding the volume between a multivariable line integral (x,y) and a single variable integral along the x axis, does this look right? ( Volume ∫0,0x+h,yf(x+h,y) ∫0,0x+h,0f(x+h) - Volume ∫0,0x,yf(x,y) ∫0,0x,0f(x) ) / h = ∫x,0x,y f(x,y) In particular I'm looking at f(x,y) parabaloids in the format z=axn+bym if that makes a difference; you can assume that f(x,y)-f(y)=f(x) I don't know if that's right or not, I was thinking of the volume as consisting of infinitesimal integral prisms, and following that the volume of a prism is its base multiplied by its height, the difference in volume from one of the infinitesimal integral prisms divided by h would equal the…

So, this pertains to a somewhat personal issue, but I have been freaking out over the possibility of my girlfriend's birth control malfunctioning. I'm worried because, though it's said that BC is 99% effective, there is a 1% chance of pregnancy. So, is there a law of probability that says in the occurrence of a scenario, that the 1% possibility HAS/WILL to happen? I doubt I'd be the unlucky 1% over the course of a month..but think of the amount of intercourse over a 10 year period using BC. You're going to have to be that 1% eventually, right? ~EE

The formula for 'n choose r' implies that r! divides n(n-1)(n-2)...(n-r+1). I seek a direct, arithmetical proof of this. Tbhank you.

Please see the attached file. Many thanks, T. question_max_functional.pdf

Hi, I'm a biologist working with emission of trace gases. I've made an experiment with warming and shading treatment to see how this affects the emission from plants. Warming causes emission to increase and shading the emission to decrease. Based on the warming treatment I've calculated the Q10 value which describes the factor by which the emission rate increases with a 10 °C rise in temperature. Now I want to know how much of the emission decrease in the shading treatment was caused by drop in temperature. I've however gotton stuck on some calculations rules and hope some one can point me in the right direction. I've attached the equations. Thanks a lot in ad…

Hi. I came across the following relation. Given two vectors v1 and v2, their exterior product is related to their tensor product by the relation [latex]v_1 \wedge v_2 = v_1 \otimes v_2 - v_2 \otimes v_1[/latex] which expands for three vectors [latex]v_1,v_2,v_3[/latex] as [latex]v_1 \wedge v_2 \wedge v_3 \wedge=v_1\otimes v_2\otimes v_3-v_2\otimes v_1\otimes v_3 +v_3\otimes v_1\otimes v_2 - v_3\otimes v_2\otimes v_1+v_2\otimes v_3\otimes v_1 - v_1\otimes v_3\otimes v_2[/latex] I get the basic idea of the exterior and tensor products but I don't know the notation for the right hand side permutation sum/product/whatever. The left side of the equation will b…

I have a problem with the following inequality : I can go as far: But i have problem with 0=ΑΒ > A=0 ή Β=0 part.

Say I have f(x) and then I have Σ(f(x))dx (I'm using Σ in place of an integral since there's no character for an integral that fits on one line), is there some formula relating Σ(f(x))dx to f^-1(x)? Sort of like the opposite of the derivative rule for inverse functions?