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if x,y,z are real numbers satisfying the relations \[ x+y+z = 1\quad\textrm{and}\quad\arctan x+\arctan y+\arctan z =\frac{\pi}{4}, \] prove that $ x^{2n+1}+y^{2n+1}+z^{2n+1}= 1 $ holds true for all positive integers n . ...
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Didnt want to make the previous thread tooo long..http://targetiit.com/iit-jee-forum/posts/inequalities-sikhna-chahte-ho-to-sikho-varna-koi-b-11546.html so new questions in new thread... This is season 2 of "Inequalities Sikh ...
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*Image* *Image* ...
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Didnt want to make the previous thread tooo long..http://targetiit.com/iit-jee-forum/posts/inequalities-sikhna-chahte-ho-to-sikho-varna-koi-b-11546.html so new questions in new thread... This is season 2 of "Inequalities Sikh ...
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Didnt want to make the previous thread tooo long..http://targetiit.com/iit-jee-forum/posts/inequalities-sikhna-chahte-ho-to-sikho-varna-koi-b-11546.html so new questions in new thread... This is season 2 of "Inequalities Sikh ...
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Didnt want to make the previous thread tooo long..http://targetiit.com/iit-jee-forum/posts/inequalities-sikhna-chahte-ho-to-sikho-varna-koi-b-11546.html so new questions in new thread... This is season 2 of "Inequalities Sikh ...
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Find ALL Polynomials satisfying [P(x)]2=1+xP(x+1) For beginners ; ...
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let 'f' be a twice differntiaible function such that f''(x)= - f(x) and f'(x)= g(x) for all x ε R. If h'(x)=[ f(x)]2 +[ g(x) ]2 , h(1)= 8; h(0) =2 then h(8) = a. 16 b. 32 c. 40 d. 50 ...
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let 'f' be a twice differntiaible function such that f''(x)= - f(x) and f'(x)= g(x) for all x ε R. If h'(x)=[ f(x)]2 +[ g(x) ]2 , h(1)= 8; h(0) =2 then h(8) = a. 16 b. 32 c. 40 d. 50 ...
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let g(x) be a continous function for all x ,and f(x) = f(a) +(x-a)g(x) for all x ε R , then a. f(x) is necessarily differentiable at x =a b. f(x) is not necessarily differentiable at x=a c. f(x) is not necessarily continous ...
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im stuck at this one [41] Find f(x) if f(x + y) = x. f(y) + y. f(x) and f '(0) = 1 ...
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let Pn = aPn-1 -1 for all n= 2,3,4,.. and let P1= ax-1 where a ε R+ then evaluate the limit lim ( x → 0 ) Pn/x ...
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f(x)= (2x4 - 14x2 - 8x +49)/(x4-7x2-4x+23) ...
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prove that \frac{1}{15}<\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.\frac{7}{8}........\frac{99}{100}<\frac{1}{10} ...
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prove that \frac{1}{15}<\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.\frac{7}{8}........\frac{99}{100}<\frac{1}{10} ...
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here's a nice one i came across while reading a book yesterday prove for all positive integers m, the integer next greater than (\sqrt{3}+1)^{2m} contains 2^{m+1} as a factor ...
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1] Let a,b,c be non-negative real numbers such that a+b+c=3. Prove that \frac a{a+2bc}+\frac b{b+2ca}+\frac c{c+2ab}\ge1 ...
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Velocity of CM of two particles is v & the sum of the masses of two particles is m. Kinetic energy of the system : A. will be = 1/2 mv2 B. will be always less then 1/2 mv2 C. will be greater than or equal to 1/2 mv2 D. will a ...
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1] Let a,b,c be non-negative real numbers such that a+b+c=3. Prove that \frac a{a+2bc}+\frac b{b+2ca}+\frac c{c+2ab}\ge1 ...
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∫(x3m+x2m+xm)(2x2m+3xm+6)1/mdx note: do without using integration by parts ...
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∫(x3m+x2m+xm)(2x2m+3xm+6)1/mdx note: do without using integration by parts ...
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1] Let a,b,c be non-negative real numbers such that a+b+c=3. Prove that \frac a{a+2bc}+\frac b{b+2ca}+\frac c{c+2ab}\ge1 ...
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we are given 201 different numbers such that sum of any 100 numbers is less than the sum of remaining 101 numbers. prove that all the numbers are positive . ...
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1] Let a,b,c be non-negative real numbers such that a+b+c=3. Prove that \frac a{a+2bc}+\frac b{b+2ca}+\frac c{c+2ab}\ge1 ...
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1] Let a,b,c be non-negative real numbers such that a+b+c=3. Prove that \frac a{a+2bc}+\frac b{b+2ca}+\frac c{c+2ab}\ge1 ...
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Draw the graph of x.e1/x ...
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Draw the graph of x.e1/x ...
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k of spring 200 N/m. Find max. extension of spring-- *Image* ...
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Ball 1 collides on with another ball 2 at rest as shown in the figure. For what value of e will the velocity of the 2nd ball be twice that of 1st after collision A.1/3 B.1/2 C.1/4 D.1/6 u1 is not given.. how to do ?? *Image* ...
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\frac{4y^{2}}{4y^{2}+1}=z \frac{4z^{2}}{4z^{2}+1}=x \frac{4x^{2}}{4x^{2}+1}=y ...
