Recently Active Mathematics Questions

This qsn cud have been in the MO section, but it's way easier than an Olympiad problem, as such. Define a function f over the set of naturals as f(n)=n! Now let a positive real a have the decimal representation as a=0.f(1)f(2 ...

Let a1=0 and a2=1. an= n/2 an-1+ n/2 (n-1)an-2+(-1)n(1- n/2 ). Find f=an+2 nC2an-1 +3 nC3an-2+...+na1. ...

Prove that for all real a,b and c satisfying: a^3+b^3=c^3 the following inequality holds: a^2+b^2-c^2> 6(c-a)(c-b) ...

let y=f(x) be differentiable function for all x belongs to R . then which one of the following is always true : (a) d2y/dx2 - (dx/dy)3 =0 (b) d2y/dx2+ (dy/dx).d2x/dy2 =0 (c) d2y/dx2 - (dy/dx)3 = 0 (d) none of these ...

hey friends wht will be the differention for {x} and [x]?????? further,,, hw will u diff y = {x}/[x] {.} represents fractional part of x [.] represents greatest integer of x ...

Lim (n → ∞) <summation> r=1 to n tan-1 ( 1/r2+3/4 ) plz help me out in this..... facing a bit prob... ...

ltn---∞ cos( x/2 ).cos( x/4 ).cos( x/8 ).................cos( x/2n ) find the value.... ...

ltx---∞ { x-sinx/x-cosx }1/2 ...

(1) The no. of solutions of the equation 2^{\left|x \right|}\left(\sqrt{1-x^{2}} \right)=1 is ? (2)The order of the differential equation y=C_{1}e^{x+c_{2}}+C_{3}e^{x+c_{4}} + C_{5}\sin (x+C_{6})+C_{7}\cos (x+C_{8}) is equal ...

Consider a parabola y=\frac{x^{2}}{4} and the point F (0, 1). Let A1(x1, y1), A2(x2, y2), A3(x3, y3),........, An(xn, yn) are 'n' points on the parabola such xk > 0 and <OFA_{k}=\frac{k\Pi }{2n} (k=1,2,3,....,n) . Then ...

ltx→0+ xm(log x)n where m,n are natural no.s find the value.... ...

1) Consider two functions f(x)=1+ e^{\cot ^{2}x} and g(x)= \sqrt{2\left|\sin x \right|-1}+ (\frac{1+\cos 2x}{1+ \sin ^{4}x}) Statement-1: The solutions of the equation f (x) = g (x) is given by x=(2n+1)\frac{\Pi }{2} for all ...

1.) limn→∞ [1/n+ n2/(n+1)3+ n2/n+23.... 1/8n ] 2.) lim 1/n[sec2π/4n+ sec22π/4n...sec2nπ/4n] n→∞ 3.) limn→∞ *Image* ...

Prove that 1/1001 + 1/1002 + 1/1003 +...................+ 1/3001 lies b/w 1 & 4/3 ...

can ne1 explain me how is it that Lim (x→0) [ sin x/x ] = 0 nd similar case for tan x [.] is GIF.... wht is the value of [cos 0] .... is it 0 or 1.... i m confused// ...

1) If f(x) = x2 - x3 find f -1(x) 2) The remainder when the polynomial x+x3+x9+x27+x81+x243 is divided by x2 -1 3) If | x | + x + y =10 x + | y | - y =12 find x + y ...

If P(x) be a polynomial such that P(x2+1) = {P(x)}2+1 and P(0) = 0 then P'(0) is equal to : (a) 1 (b) -1 (c) 0 (d) none ...

Number of quadratic equations with real roots which remain unchanged even after sqaring their roots is 1. 1 2. 2 3. 3 4. 5 ...

find the period of following function: f(x+\lambda ) = 1 + \sqrt{2f(x) - f^{2}(x)} i have a doubt in answer ...

find coefficient of x49 in expansion of (x+1)(x+2)(x+3)......(x+99) ...

Find ax5 + by5 where a,b,x,y are real numbers satisfying ax+by = 3 ax2+by2 = 7 ax3+by3 = 16 ax4+by4 = 42 ...

what will be Lim (x→∞) (x+2)tan-1(x+2) + xtan-1x i m 'ving doubt in this..... plz help ...

A function f(x) is a polynomial function in sin-1x ( ie f(x) = a(sin-1x )n + b(sin-1x )n-1 + c(sin-1x )n-2..........+ k) the conditions given on f(x) are: 1. f(x) is an onto function. 2. f o f o f o f o f o f o...........o f ...

check given function f(x)=Ix+2I verifies lagrange's theorem on :- a) [-2,4] b) [-3,4] c) none of these here I DENOTES MODULUS.... ...

find limit n tends to infinity ( 1/1.4 + 1/4.7+..........+1/ (3n-2) ( 3n+1) ...

Find least no. of digits in x , When f(f(f(f(x)))) = 1 whre f(x) is the sum of the digits in x x > f(x) f(x) > f(f(x)) f(f(x)) > f(f(f(x))) > 1 ...

can ne1 plz explain me in brief how can we draw the graph of h(x) = f(x) + g(x) i.e., the sum of two functions...... e.g., y = x+sin x y = x2+x3 y= x + 1/x is dere any direct approach for such graphs or we need to find maxima ...

Hey friends.... facing a bit prob in finding summation... plz help lim(n→∞) <summation>r=1 to n ( r/4r2+1 ) i think the answer shud be ∞ as the degree of Nr is less than the degree of Dr..... plz let me know my mi ...

prove 4 cos2∩/7 . cos∩/7 -1 = 2cos2∩/7 ...

Hey frnds.... plz help me out here........ i tried to do in a graphical method.... but can't succeed..... f(x) = [x] + 1 , x≠nπ ; n= 0 , + - 1 , + -2,...... = 3 otherwise g(x) = x2+1 ; x≠3,x≠0 3 ; x=0 5 ; x=3 then... L ...