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UNITED BOOK HOUSE-MISCELLANEOUS EXERCISE-EXERCISE
- Evaluate : underset(nrarrinfty)lim [1/n + 1/(n+1)+ 1/(n+2) + .... +1...
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- Solve: xdy-ydx= sqrt(x^2+y^2)dx.
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- Solvex dy + y dx = (ydx - xdy)/(x^2 + y^2)
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- Solvex cos x dy/dx + y (sin x + cos x) = 1
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- Solve(cos y + y cos x ) dx + sin (x - x sin y) dy = 0
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- Solve(d^2y)/(dt^2) = tan y sec ^2 y, given dy/dt = 0 when y = 0
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- Prove that cos (sinx) > sin (cos x) for all x in 0 le x le pi//2
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- If the line ax+by+c=0 is a normal to the curve xy=1 then
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- Prove that all points of the curve y^2=4a[x+asinx/a] at which the lang...
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- Find the point on the curve 4x^2 + a2y^2 = 4a^2, 4 < a^2 < 8 that is f...
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- The area bounded by the parabola y = x - x^2 and the line y = mx equal...
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- Prove that f(x)= sin x+sqrt 3 cosx has maximum value at x=pi/6
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- The length of the hypotenuse of a right angled triangle is 3 ft. Find ...
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- The angle between the tangents to the curves y=sin x and y = cos x at ...
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- Show that f(x) = (x-2)e^x + x + 2 is positive for all positive values ...
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- Vectors vecm, vecn, vecr are such that vecm + vecn + vecr = 0, prove t...
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- If vecp xx vecq = vecm xx vec n and vecp xx vec m = vecq xx vecn, sho...
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- If veca xx vecb + vecb xx vecc + vecc xx veca = 0. Show that the vecto...
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- The vector vecr is collinear with vector vecn = 2hati + hatj + 3hatk ...
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- If veca,vecb and vecc are three mutually perpendicular vectors of equa...
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