Recently Active Mathematics Questions

The line joining A(b cosα , b sinα) and B( a cosβ,a sinβ) is produced to point M(x,y) so that AM:MB = b:a, then what's the value of x cos α+β/2 + y sin α+β/2 ???? ...

$\textbf{In a $\mathbf{\triangle ABC},$ Prove that }$\\\\ \mathbf{\frac{1+Cos\;B\cdot Cos\;C}{1+cos \;A}+\frac{1+Cos\;C\cdot Cos\;A}{1+cos \;B}+\frac{1+Cos\;A\cdot Cos\;B}{1+cos \;C}\geq \frac{5}{2}}$ ...

1+ 2+ 3+ 4+.......∞ how to evaluate dis?? ...

Show that : sin5x+cos5x+sin4x≤2 for all values of x, ...

Q: Let f : [0,1] → R is a continuous function such that \int_{0}^{1}{f(x) dx=0} . Prove that there is some ' c ' ε (0,1) such that \int_{0}^{c}{f(x) dx} = f(c) ...

Q: (x4y2-y) dx + (x2y4-x) dy = 0 Q: \int \frac{x dx}{log x . sec x} ...

Let f be twice differentiable in [0,2]. show that if f(0)=0,f(1)=2, f(2)=4, then there is an 'x' in (0,2) such that f''(x)=0 ...

Determine all pairs (a,b) of positive integer such : a2/2ab2-b3+1 positive integer ...

Here an Isosceles triangle is inscribed in a square. The angle A is given by 15 degree... prove that the triangle formed below is an equilateral triangle. *Image* ...

1)Find all function from +ve reals to the same satisfying f(f(x)-x) = 2x for all x>0 2) f is a function from the set of natural numbers to the same. satisfying f(n+1)>f(f(n)) for all natural number n. Prove that f(n) = ...

Use the mean value theorem to prove that |sinx-siny| ≤|x-y| for all real numbers x,y ...

fin ...

What is the nth term of 1,2,3,6,24,108 ......? ...

A triangle has all its sides as integers marked l,m,n with l>m>n. Also given that \left\{\frac{3^l}{10^4} \right\}=\left\{\frac{3^m}{10^4} \right\}=\left\{\frac{3^n}{10^4} \right\} Find the minimum perimeter of the tria ...

\int \left(tan^{-1}x \right)^{2}dx ...

A lighthouse, facing north, sends out a fan-shaped beam of light extending fron north-east to north-west. An observer on a steamer, sailing due west, first sees the light when he is 5 km awayfrom the lighthouse, and continues ...

By using the concept of slope, prove that the diagonals of a rhombus are at right angles. ...

Let f(x) be a continuous function such that f(x) does not vanish for all real values of x if *Image* then f(x) (for all x ε R) is (a) an even function (b) an odd function (c) a periodic function (d) None of these Ans: (d) ...

sin^3x+sin^2x+sinx=1 ...

If x,y,p satisfy x2+y2=p where p is a prime (4k+1) Then prove that the above equation has one and only one solution in Z ...

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What's d solution of log(a-bx) ????????????????? ...

Is it possible to find a continuous function defined over all real numbers such that its graph intersects any non-vertical line in infinitely many points? ...

value of a for which the equation 4cosec2[pi(a+x)]+a2-4a=0 has real roots..... ...

Find all continuous functions f:\mathbb{R}\to [1,\infty) for which there exist an a\in\mathbb{R} and k , a positive integer, such that f(x)f(2x)\cdots f(nx)\le an^k for every real number x and positive integer n. ...

Given are three real numbers a,b,c. satisfying abc+a+c=b. Prove that 2/a2+1 - 2/b2+1 + 3/c2+1 ≤ 10/3 . Can the equality hold? PS. This does not require any inequality theorem(not even Am-Gm). I cant claim to have solved thi ...

find all integers a such that (x+a)(x+1991) + 1 can be written as (x+b)(x+c) where b and c are integers themselves. it implies that we have to find all integers a , b and c such that 1991 + a = b + c and 1 + 1991a = bc for so ...

If x,y,z≥0 and x2+y2+z2=3 Find the max for the expression F=xy+xz+yz+ 5/x+y+z ...

pls someone help me..in the graph f(x)=1/x(reciprocl function of x) we observe that x(tends) -- 0+ then f(x) -- +infinity and x--0(minus) then f(x)-- minus infinity and when x tends to plus or minus infinty then f(x) tends to ...

Show that : tan2 π/7 +tan2 2π/7 +tan2 3π/7 =21 ...