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Write 271 as the sum of positive real numbers so as to maximize their product more of calculus than algebra[4] ...
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\int {e^{x\sin x+\cos x}}\left(\frac{x^4\cos^3x-x\sin x +\cos x}{x^2\cos^2 x} \right)dx ...
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[4] nice one! *Image* ...
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\sum_{r=0}^{9}{\left(-1 \right)^r\cos^{10}\frac{r\pi}{10}} any short solution using complex? ...
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\sum_{r=0}^{9}{\left(-1 \right)^r\cos^{10}\frac{r\pi}{10}} any short solution using complex? ...
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animation oh hcv problem *Image* ...
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find : \ \int_{0}^{\pi}\frac{\cos nx}{2-\cos x}dx\ (n = 0,\ 1,\ 2,\ \cdots) ...
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please solve it asap *Image* x ...
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please prove these identities : $ \sin (\frac{\pi}{2m})\sin (\frac{2\pi}{2m})\sin (\frac{3\pi}{2m})\dots\sin (\frac{(m-1)\pi}{2m}) =\frac{\sqrt{m}}{2^{m-1}} $ \sin (\frac{\pi}{4m})\sin (\frac{3\pi}{4m})\sin (\frac{5\pi}{4m})\ ...
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http://www.youtube.com/watch?v=mzKmGTVmqJs ...
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THIS QUESTION WAS SOLVED BY MY SIR LAST YEAR ,BUT STILL I AM NOT SATISFIED WITH THE SOLUTION I HOPE I WILL GET SOME AWESOME ANSWERS IN THIS FORUM *Image* a particle of mass m , charge q is released from -∞ along +ve x axis ...
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z=\frac{3}{2+cos\theta + i \sin\theta } the locus of z is ? ...
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i feel that the question has some printing errors i am typing the question as given in the book consider \ the \ sequence \ x_n \ defined \ by \ \\ x_1 = \frac{1}{2} ,x_{n+1}=x_n^2 + x_n \\ define \ S = \frac{1}{x_1 +1}+\frac ...
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find the product \frac{(1^4 +\frac{1}{4})(3^4 +\frac{1}{4})(5^4 +\frac{1}{4}).......(49^4 +\frac{1}{4})}{(2^4 +\frac{1}{4})(4^4 +\frac{1}{4})(6^4 +\frac{1}{4}).......(50^4 +\frac{1}{4})} ...
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let S={1,2,3,.......,100} the number of unordered pairs (A,B)of subsets of S such that A and B have no ekements in common , where A or B both may be φ(null set) is ? answer : \frac{3^{100} + 1}{2} the no.of order pair is 310 ...
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if \ a+b+c =1 ,; a,b, c \rightarrow R^+ \\ prove \ that \ \\ \\ \sum_{cyclic}{} {\frac{a}{1+bc}}\geq \frac{9}{10} ...
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*Image* P.S the springs are attached to string and x=a ...
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A fair coin is tossed n times. Let P n denotes the probability that no two (or more) consecutive heads occur in n tosses. ...
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prove that the equation x3-2x+1=0 has roots as √2sin(π/4),2sin(π/10),2sin(3π/10) q is from adg ...
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*Image* i dont have the answer ...
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A stack of 2000 cards is labeled with the integers from 1 to 2000, with different integers on different cards. The cards in the stack are not in numerical order. The top card is removed from the stack and placed on the table, ...
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not a doubt if a digit is removed frrom the left of a natural number n, the resultant is n/57 find the sum of digits of n ...
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x=\sum_{n=3}^{100}{\frac{1}{n^2 -4 }} \\ \color{red}then \ find \ [x] my answer is coming out to be -3 ...
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how many necklace can be using 8 stones 2- red 3-blue 3-black ...
