e^pi < pi^e, True or False?
443040
I don't know why 4 of the 8 answers so far say it's true. It's false.\nOne of them reversed the inequlity, and so gave the wrong answer.\ne=2.71828182845905\npi=3.14159265358979\n\ne^pi=23.1406926327793\npi^e=22.459157718361\n\ne^pi < pi^e is false\nChecking to 510 decimal places won't change the result.
254898
i think it isn't.\n\nsin x has a period equal to pi or 2 * pi (i am not sure). The value has to repeat itself.\ncos x has period = 2 * pi\n\nsinh x isn't a periodic function. It is an exponential curve, so having no periodicity. \n\nso the given function is not periodic.
184348
if 'i' means the imaginary unit....\ni = e^(i*pi/2) = cos(pi/2) + i*sin(pi/2)\nsquare root of i\n(i)^(1/2) = e^(i*pi/4) = cos(pi/4) + i*sin(pi/4)\ncube root of i\n(i)^(1/3) = e^(i*pi/6) = cos(pi/6) + i*sin(pi/6)\nand so on.......
937153
B is false: Let a be any number other than zero. If a>0, 2(2a)-a > 0, and f'(2a) = 2. Conversely, if a<0, 2(2a)-a<0, and f'(2a) = -2. Thus, any value of a other than zero serves as a counterexample.\n\nA is also false, although I'm not sure your teacher knows this. She may be thinking of something like f(x)=[a, b]∫g(t) dt, which is alawys a constant function regardless of g(t), and thus its derivative is zero. However, if the free variable appears in the limits of integration, the function may be nonconstant: for instance, let f(x) = [1, x]∫1/t dt, which is equal to ln x for positive values of x, and its derivative is certainly not zero. So the correct answer here is d: both A and B are false.
618692
the correct option is e \n the value of i radian is 180/pi = 57.3248 ( if pi is 3.14)
791247
You are correct about the conversion; however, the use of 'pi' is indicative of radians.
236568
Pi is indeterminate.  It keeps going on forever.  Here is the beginning:\n\n3. 14159 26535 89793 23846\n\nThe last link is supposed to list the first 50,000 digits.  I didn't check to see if it was right :).
1147102
pi*(r^2)\n\nIt doesn't matter which unit you use, just make sure you're consistent.
173341
Crap!\n\nSomething to do with Pi.  When my friend was in college she used to say the first one.\n\nETA:  They are both frases said to remember the numerics of Pi.
96413
Actually, there are rather sophistocated ways of proving that pi is irrational, which means that it can never be written completely in decimal form. I have seen a proof before, but the concepts were too difficult for me to grasp. Therefore, we ARE SURE that pi can never be fully expressed as a decimal expansion, i.e. it will go on forever with no repeating pattern.\n\nHere is just one web example for the proof. \n\nhttp://www.lrz-muenchen.de/~hr/numb/pi-irr.html
1042552
Here is my proof. Suppose P(x) is a polynomial in odd degree, for example 4x^5 + 3x^4 - 5x^3 + 2x^2 - 6x + 9. For large enough values of x, the term in x^5 will be so much larger than any of the other terms that it will swamp the smaller powers of x, and x^5 alone will determine the value of P. \n\nNow, if P is of odd degree and x is very large and positive, P will be positive; if x is very large and negative, then P will be negative. Therefore, somewhere between these two values of P there must be at least one point where P = 0. QED.
1130864
u(x, y) = e^(pi) e^x cos(ny)\n\nu_x (x, y) = e^(pi) e^x cos(ny)\n\nu_xx (x, y) = e^(pi) e^x cos(ny)     since e^(pi) cos(ny) is "constant" with respect to x\n\nu_y (x, y) = e^(pi) e^x (-nsin(ny))\n\nu_yy (x, y) = e^(pi) e^x (-n^2cos(ny))\n\nu_xx (x, y) + u_yy (x, y) = 0\n= e^(pi)(e^x)cos(ny)(1 - n^2)\n\nTherefore, u(x, y) is harmonic only if 1 - n^2 = 0, which is equivalent to n = 1 or n = -1.  For other values of n, we see that u(x, y) is, in general, not harmonic.\n\nTo find the harmonic conjugate v(x, y) of u(x, y) (for each of the cases n = 1 and n = -1), use the Cauchy-Riemann equations.\n\nThen use f(z) = f((z,0)) = u(z,0) + i v(z,0) to try to express w = u + iv in terms of z = x + iy (i.e. set y = 0 in u(x,y) and v(x,y), substitute into w = u(x, 0) + i v(x, 0)).
474968
The Watt is a unit of Power.\n\n(I'm pretty sure P does not equal vf though)\n\nEDIT - No you're right. I had to work it out for my own peace of mind though!\n\np=e/t\nw(e)=fd\np=fd/t\np=f(d/t)\np=fv
706332
The antiderivative is:\n\n(1/2)erfi(sqrt(pi)*x)\n\nI used Wolfram
236956
pi times the radius squared
932970
try this\nhttp://en.wikipedia.org/wiki/Pi
634042
Theres a poster in my maths class that says "a trillion steps towards an infinitae pi" So i assume the best so far is a trillion number after the decimal point. WOW!