Recently Active Mathematics Questions

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Find all real numbers a\in(-2,2) satisfying the following condition: The polynomial x^{154}-ax^{77}+1 is a multiple of the polynomial x^{14}-ax^{7}+1 . ...

if f(x+y)+f(x-y)=2f(x)f(y) for all x,y ε R and f(0)≠0 then prove that f(x) is an even function. ...

*Image* =? Edit:- denom is 1+sin2√θ ...

On my calculator screen, the number 2659 can be read upside down as 6952.The digitsthat can be read upside down are 0,1,2,5,6,8,9 and are read as 0.1.2.5.9.8.6 respectively.Starting with 1, the fifth number that can be read u ...

In a \Delta ABC , let x=\tan\left(\frac{B-C}{2}\right)\tan\left(\frac{A}{2}\right) y =\tan\left(\frac{C-A}{2}\right)\tan\left(\frac{B}{2}\right) z =\tan\left(\frac{A-B}{2}\right)\tan\left(\frac{C}{2}\right) Prove that x+y+z+x ...

Solve for natural 'k', x2+y2+z2=kxyz, x,y,z are naturals. ...

x=∩/2 is a point of ?????? whether local max. por local minimum considering n odd or even ...

lim x-infinity 1/n(tanpi/4n +tan2pi/4n+..........tan npi/4n) equals... is it '2pilog2'? ...

Q1.Prove that the orthocentre of the triangle formed by any three tangents to the parabola lie on the directrix. Q2.If a normal to a parabola makes an angle θ with the axis ,show that it will cut the curve again at an angle ...

g(x) = ∫ cos4t dt , then g(x+π ) = ? { lower limit =0 upper limit= x} a. g(x) + g(π) b. g(x) - g(π) c.g(x) *g(π) d. g(x)/g(π) ...

lim x→0 sinxn/(sinx)m= ?? where m<n ...

k is a positive integer and | x | < 1 What is \lim_{n \to \infty} xn nk = ? answer supposd to be 0 ...

the value of \int_{-5}^{10}{f(x)dx} if f(x)=e^{2secx}ln(1+sinx/1-sinx) if -5\leq x\leq 5 5≤x≤5 f(x)=1 otherwise ...

let f: R→R f(x)= x x is irrational 1-x x is rational ...

prove that if 2n - 1 is prime then n is also prime ...

This functional equation is nice and has a super short and elegant solution: Find all functions f: N --> N such that xf(y) + yf(x) = (x + y)f(x2 + y2) for all x, y and in N, where N = {0, 1, 2, 3, ...}. ...

if f(x)= sin-1([x]+x)/[x] ,[x]≠0 = 0 ,[x]=0 then find lim f(x) x→0 ...

what are inseterminates in limits chapter?give list of them ...

Let a and b be 2 coprime +ve integers and f(x) =[x] (greatest integer function). show that \sum_{n=1}^{b-1}{f\left( \frac{na}{b}\right)}=\frac{(a-1)(b-1)}{2} ...

g(x) = ∫ cos4t dt , then g(x+π ) = ? { lower limit =0 upper limit= x} a. g(x) + g(π) b. g(x) - g(π) c.g(x) *g(π) d. g(x)/g(π) ...

g(x) = ∫ cos4t dt , then g(x+π ) = ? { lower limit =0 upper limit= x} a. g(x) + g(π) b. g(x) - g(π) c.g(x) *g(π) d. g(x)/g(π) ...

g(x) = ∫ cos4t dt , then g(x+π ) = ? { lower limit =0 upper limit= x} a. g(x) + g(π) b. g(x) - g(π) c.g(x) *g(π) d. g(x)/g(π) ...

It is not of this year... ABc is a triangle with AB=AC...D is the mid-point of BC, P is any other point on AD. PE is perpendicular to AC. \frac{AP}{PD}=\frac{BP}{PE}=\lambda \\ \ \frac{BD}{AD}=m\\ \ z=m^2(1+\lambda)\\ \text { ...

Q1 lim [x2]+[(2x)2]+....[(nx)2]/n n→∞ Q2 check continuity of f(x) on [1,3] f(x)=[x2+1] ...

My friend gave me this question.. For n\ge2 Prove that 1 - \frac{1}{2}+\frac{1}{3} - ... \pm \frac{1}{n} is not an integer. ...

A 10 X 10 X 10 cube is formed of small unit cubes. A grasshopper sits at the center O of one the corner cubes. At a given moment it can jump to the center of any of the cubes which has a common face with the cube where it sit ...

Let z_1,z_2,z_3 represent vertices A,B,C of a right angled triangle,right angled at C,if AC = 1 unit and (z_1-z_2)^2 = 2 (z_1-z_3)(z_2-z_3)(-1 + i ) ,find angle A ...

For the ellipse 2x^2-2xy+4y^2-(3+root(2))=0...the inclination of major axis of it with x axis is ...

how we will draw d graph of sin x and sin2??? ...