Recently Active Mathematics Questions

Consider (n+1)n/nn+1 (1+1/n)n < 2 +1/2 + 1/22 + 1/23 + ...... ∞ = 3, provided n>3 Please explain me the above step. I can prove that the expression in LHS is greater than 2 by Binomial expression. How does this come? ...

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find f(x) if f(x+y)=f(x)+f(y) such that f(x) is continuous at 0. ...

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in which ratio the line 3x+4y+2=0 divides the distance between between 3x+4y-5=0 and 3x+4y+5=0?? ...

i request u guys if u can provide a few problems and their solution based on taylor and maclaurian series within constraints of jee,of course thanx a ton! ...

If the integers m and n r chosen at random with replacement frm 1 to 100 , then what is the probability that a no. of the form 7^m + 7^n is divisible by 5? ...

if f(x+y)=f(x)g(y)+g(x)f(y) and g(x+y)=g(x)g(y)-f(x)f(y) prove that f(0)=0 and g(0)=1 ...

p is the probability that a man aged x years will die in a year.find the probability that out of n men A1,A2,.......,An each aged x years,A1 will die in a year and will be first to die. ...

If F''(x) + F(x) = 0 F'(0) = 0 F(0) = 0 prove that F(x) = 0 for all real x ...

find the area of the ellipse given by the equation x2/a2 + y2/b2 = 1 ...

lim(x→0) (sin xn)/x = pi/180 for n=? ...

Range of the function f(x)=ln[cosxcosx+1],xE(0,pi/2) (A)(ln(1+e 1/e ),ln2) (B)(ln(1+ 1/e 1/e )ln2) (C)(0,ln2) (D)None of these Ans.(B) is the correct choice. ...

q1)fna and gna exist and are not equal for some n . Further if f(a)g(x) - f(a) - g(a)f(x) +g(a) =4 g(x) - f(x) then value of n is: ans is 4 how?? lim ( 1+24+34+........n4 - lim 1+23+33+........n3 ) n→∞ n 5 Q2)expansion of ...

*Image* The side of the square is 1 unit and the circles have diameter as 1 unit.. ...

Prove that 100400 can be written as the sum of two squares of integers....!! Such an easy one....... but a good one though.......!! ...

1.If A and B are two distinct matries such that A3=B3 and A2B=B2A,find the det(A3+B3) and det(A2+B2). 2.Suppose A and B are two non-singular matrices such that B≠I,A6=I and AB2=BA.find the least value of k for Bk=I. ...

If x1,x2 are the roots of x2-3x+a=0, and x3,x4 are those of the equationx2-12x++b=0, and x1,x2,x3 and x4 are in increasing G.P.,find a and b. ...

Show that C12 - 2C22 + 3C32............-2n.C2n2 = (-1)n-1.nCn where Cr stands for 2nCr ...

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I don't know how to solve it, But I thought it will be nicer for those who know how to solve it : *Image* ...

for x in [-pi,pi] solve: *Image* this is wat my book says....but i m surprised by equation -cos x =cos x??? experts help!!!! ...

sorry for wasting one thread of tiit...plz delete this one nishant bhaiya! ...

z1,z2,z3 are three complex numbers such that (z3-z1)/(z3-z2)=∂ find ∂ such that it represents an equilateral triangle i got 0.5±i√3/2 as the answer.in fact these both were in the options too.but the final answer was gi ...

what is the probability that sin-1 ( sin x ) + cos-1 ( cos y ) is an integer x , y belongs to { 1 , 2 , 3 , 4 }? ...

i am from 10 std. i got 35 marks in rmo and was selected for inmo on 6th feb 2011.how should i prepare?please help ...

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write following functions as a function g(w) where w=(z+z-1) (1)f(z)=z10+z9+z8+....+z+1 (2)f(z)=z8-z7+z5-......+z3-z+1 ...

The conditions of two functions being equal: (1)Ranges should be equal (2)Domains should be equal Now my doubt is, let one function be sinx and the other be cosx,then we have the ranges and the domains of both the functions t ...