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A DAS GUPTA-Miscellaneous Exercises-Exercise
- f: [0.4]-> R is a differentiable function. Then prove that for some a,...
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- Given a function f:[0,4]toR is differentiable ,then prove that for som...
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- If f: R to [0,∞) be a function such that f(x -1) + f(x + 1) = sqrt3(f...
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- Using Rolles theorem, prove that there is at least one root in (45^(1/...
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- A=[(a,1,0),(1,b,d),(1,b,c)],B=[(a,1,1),(0,d,c),(f,g,h)],U=[(f),(g),(h)...
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- Find the equation of circle touching the line 2x + 3y + 1=0 at the poi...
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- (int(sin^(3/2)x+cos^(3/2)x)dx)/(sqrt(sin^(3)x cos^(3)x sin(x-alpha)))
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- T is a parallelepiped in which A,B,C and D are vertices of one face an...
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- f'(0) = lim(n->oo) nf(1/n) and f(0)=0 Using this, find lim(n->oo)((...
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- If y(x)=int(pi^2/16)^(x^2) (cosx cos sqrt(theta))/(1+sin^2 sqrt(theta)...
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- At any point P on the parabola y^2 -2y-4x+5=0 a tangent is drawn which...
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- If a DeltaABC remains always similar to a given triangle and the point...
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- Find the range of values of t for which 2sint=(1-2x+5x^2)/(3x^2-2x-1)
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- if |f(x1)-f(x2)|<=(x1-x2)^2Find the equation of gent to the curve y= f...
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- Find the equation of the common tangent to the circle x^2 + y^2 = 16 a...
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- If [(4a^2,4a,1),(4b^2,4b,1),(4c^2,4c,1)][(f(-1)),(f(1)),(f(2))][(3a^2...
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- The total number of runs scored If n matches is (n+1)/4(2^(n+1)-n-2),w...
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- A square circumscribes the circle |z -1| = sqrt2. If one of the vertic...
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- Evaluate int(0)^(pi)e^(|cosx|)(2"sin"(1/2cosx)+3"cos"(1/2cosx))sinx dx...
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- If f(x-y)=f(x).g(y)-f(y).g(x) and g(x-y)=g(x).g(y)+f(x).f(y) for all x...
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