Recently Active Mathematics Questions

*Image* from arihant ,circles ...

Draw the graph of f(x)=x+1/x ...

\int\frac{cos7x-cos8x}{1+2cos^2x}dx ...

\frac{2}{log_{4}(2000)^{6}}+\frac{3}{log_{5}(2000)^{6}} ...

Find the square of the sum of the roots of the eqn log_{3}x .log_{4}x.log_{5}x=log_{3}x.log_{4}x+log_{4}x.log_{5}x+log_{3}xlog_{5}x ...

Find x satisfying the eqn log 4 +(1+\frac{1}{2x})log3 = log(\sqrt[x]{3}+27) ...

Prove that \int_{0}^{n\Pi}{\left|\frac{sinx}{x} \right|}dx < \frac{2}{\Pi}\left(1 + \frac{1}{2} + \frac{1}{3} + ......\frac{1}{n} \right) ...

\int_{0}^{\frac{\Pi }{2}}\frac{dx}{1+cos^{2}x} In arihant, he divides Nr and Dr by cos2x which is absurd as it would be like dividing by 0 as cos2(90) =0 (90 is in the domain of x) Secondly, after this step, the integrand is ...

Evaluate \int_{-1}^{0}\frac{dx}{x^{4}-x^{2}+1} ...

Σ(n=2 to n→∞) ((n^4+3n^2+10n+10))/((2^n)(n^4+4)) ...

$Calculate $\int_{\frac{1}{2}}^{2}\frac{1}{(x^2-3x).(x^{2010}+1)}dx$ ...

1. two integers x and y ar drawn (without replacement) out of set (0,1,2,3,---,10) find the probability that -5<x-y<5? 2. Two natural numbers ( x and y) ar choosen at random. What is the probability that x^2 + y^2 is di ...

In this page: http://en.wikipedia.org/wiki/Proofs_of_Fermat%27s_little_theorem In the Second method proof that is given there: Can someone visit the page and tell me why should it be so that when a,2a,3a,.....(p-1)a when divi ...

prove that ∫01xxdx =Σ∞n=1 (-1)n+1/nn how to proceed ? ...

1. A ball moving around the circular path x2+y2-2x-4y-20 = 0 in anticlockwise direction, leaves it tangentially at the point P (-2,-2), after which it rebounds from a a straight wall,and passes through the center of the circl ...

Post some questions based on RANGE DOMAIN and functional equations! Thank u ...

i have open this thread to discuss integration questions ... so post questions and we will discuss it........... ...

Let 0 < a ≤ b. Define a1 = a+b/2 , b1 = a1 b and for each integer k≥1, ak+1 = ak + bk /2 , bk+1 = ak+1 bk . Find the limit of the sequence {bn}. That is find \lim_{n\to\infty} b_n ...

f(x) = sinx -x find area bounded by y=f-1(x) ,tangent and normal drawn to it at the points with abscissae π and 2π . ...

Let S = (z_1,z_2,...,z_{2010}) We construct for each z_i \in S the set S_i = (z_iz_1,z_i,z_2,...,z_iz_{2010}) If it is true that S_i = S for 1 \le i \le 2010 then prove that (1) |z_i| =1 (2) z \in S \Rightarrow \overline{z} \ ...

The Number of triangles which are obtuse and which have the points (8,9),(8,16),(20,25) as the feet of perpendiculars drawn from the vertices on the opposite sides is a)0 b)1 c)2 d)3 ...

$Find Max. and Min. value of $\sqrt{x^3-6x^2+21x+18}$\\\\ Where $x,y\in R$ and $-\frac{1}{2}\leq x\leq 1$ ...

\lim_{n \to \infty }n.sin(2\pi en!)= ...

1. show that the sum of a nonzero real no and its reciprocal cannot lie in (-2,2). Can we solve this by inequalities? 2.Find m so that 3x^2-2mx-4=0 and x^2-4mx+2=0 may have a common root. Can the eqns have a common non-real r ...

$\underline{\underline{Q:}}\Rightarrow $\lim_{x \to\0}\ \frac{sin(tanx)-tan(sinx)}{sin^{-1}(tan^{-1}x)-tan^{-1}(sin^{-1}x)}= ...

find the coeffcient of (x^a)(y^b) in the expansion (x+y+xy+2)^(2008), where both a and b are even nos? ...

Find all prime numbers that satisfy simultaneously p+1=2x2 p2+1=2y2 I solved it by the most elementary method can u all do the same even to prophet Sir(its not a challenge but the simplest solution actually doesnt require num ...

if x , y , z > 0 then the value of x/y + y/z + z/x lies in the interval ...

1. If a,b,c are odd integers , ax^2+bx+c=0 cannot have ratioal roots. Prove it. 2. For what values of a does the eqn (2a+1)x^2-a(x-1)=2 has one root greater than 1 and other less than 1. 3. If a and b are the roots of x^2+px+ ...

What is \huge \lim_{n \rightarrow \propto }\frac{x^{n}}{n!} ????? ans : 0 (Right now I am studying in a state engg colg. in 1st yr. I came across this qsn once in success magnet of Aakash Inst. and another time while the teac ...