Recently Active Mathematics Questions

Not dbts, but action here has slowed up a bit, so trying to bring them up.... 1) Reals x,y satisfy x^2+y^2+xy=1 . Find the minimum value of x^3y+xy^3 . 2) This is a bit common sum. (3+x^{2008}+x^{2009})^{2010} =\sum_{i=0}^{i= ...

FIND MODULUS OF sin(x+iy) ...

For what values of the parameter a does the function f (x) = x3 + 3(a − 7) x2 + 3(a2 − 9)x −1 have a positive point of maximum? Solution: f '(x) = 3x2 + 6(a − 7) x + 3(a2 − 9) For f (x) to have a maximum at some poi ...

in the recent past kaymant sir had started numerous threads which has helped many in mean value theorems so can any forum expert start a similar thread on sandwich theorem as due to their experience they wud have come across ...

Prove the following: For every real valued function f differentiable on an interval [a,b] not containing 0 and for all pairs x1 ≠x2 in [a,b], there exists a point ξ in (x1, x2) such that \dfrac{x_1f(x_2)-x_2f(x_1)}{x_1-x_2 ...

eliminate θ frm \frac{cos(\alpha -3\theta )}{cos^{3}\theta }=\frac{sin(\alpha -3\theta )}{sin^{3}\theta }=m ...

find the value of sin 2Ï€/7 + sin 4Ï€/7 + sin 8Ï€/7 7 /2 ...

Q) Evaluate \int_{0}^{1}{}(tx+1-x)^{n}dx where n is a positive integer and 't' is a parameter independent of 'x' . hence show that \int_{0}^{1}{x^{k}(1-x)^{n-k}}dx=[^{n}C_{k}(n+1)]^{-1} ...

hw do we calculate minimum distance btwn two given curves? ...

is tata mvgraw hill course in maths good? ...

This one is a very very simple one for nay one in class xi-xii but ffor the sub xi guys.. Write 105 as teh sum of consecutive integers in 8 ways... Dont just give the answer but also think why it works! ...

Plz solve this sum. If acos theta - bsin theta =c,prove that a sin theta + b cos theta= (a2+b2-c2) ...

Let f defined on [0,1] be twice differentiable such that |f''(x)|\leq 1 for all x \in [0,1] . If f(0) =f(1) , then show that |f'(x)|<1 for all x \in [0,1] i think such question need mathematically rigorous analysis like th ...

find the maximum product(approximate) of positive real numbers whose sum is 271 and also prove the result. try it very good question and very pretty answer... ...

Given that a,b are odd and c,d are even,then A. a2 - b2 + c2 - d2 is always divisible by 4 B. abc + bcd + cda + dab is always divisble by 4 C. a4 + b4 + c3 + d3 + c2b +a2b is always odd D. a +2b +3c +4d is odd ...

1. \lim_{n \to \infty} (1 + sin\frac{a}{n})^{n} 2. Function f(x) = (|x - 1| + |x - 2| + cosx), x\epsilon [0,4] is discontinuous at how many points? 3. \lim_{n \to \infty} (\frac{1}{1.3} + \frac{1}{3.5} + \frac{1}{5.7} +....+ ...

Find all pairs (x, y) of integers such that x^3 - y^3 = 2xy + 8 ...

make 4 equilateral triangles with 7sticks (all the sticks are of equal length) ...

prophet sir .. have a try at this one :) Each of the boys A and B tells the teacher a positive integer but neither of them knows the other`s number.The teacher writes 2 distince positive integers on the blackboard and announc ...

Prove that if z1 and z2 are two complex numbers and c>0 , then |z1+z2|2 ≤ (1+c)|z1|2 + (1+c-1)|z2|2 ...

\frac{9}{1!}+\frac{16}{2!}+\frac{27}{3!}+\frac{42}{4!}+... ...

For natural n>1 let 3n+1 be a perfect square. Prove (n+1) can be written as a sum of 3 perfect squares, not all of which may be distinct. ...

Suppose f be a continuously differentiable function on [a,b] and twice differentiable at x=a with f''(a) being non-zero; that is, the limit \lim_{x\to a^+}\dfrac{f'(x)-f'(a)}{x-a} exists and is non-zero. Applying LMVT to f in ...

Q1) Prove that if a function f is continuous on [a,b], differentiable on (a,b) and f(a)=f(b)=0, then for any \alpha\in\mathbb{R} , there exists some c\in (a,b) such that \alpha f(c)+f'(c)=0 Q2) Let f and g be functions contin ...

Which is greater in the following pairs? (i) e^\pi or \pi^e (that's old) (ii) 2^{\sqrt{2}} or e (iii) \ln 8 or 2. In each case your answer must be accompanied by a proof. ...

range of e^x-[x],x belong to R. ...

Q 1) Prove that f(x)=\frac{x^7}{7}-\frac{x^6}{6}+\frac{x^5}{5}-\frac{x^4}{4}+\frac{x^3}{3}-\frac{x^2}{2}+x-1 has exactly one real root Q 2) In 1 hour a snail travels 60 meters. Prove that there was an Interval of 10 minutes w ...

if tan a=1/1+2^-x and tan b=1/1+2^x+1, then write the value of a+B lying in the interval(0,90). ...

Find the limit: \lim_{x\to\infty}\left(\sin\sqrt{x+1}-\sin\sqrt{x}\right) (you must supply a proof for your answer.) ...

if sinx+cosec x=2then the value of sin ^n +cosec^n=? ...