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V PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
- Find the second order derivative of the function tan ^(-1)x
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- Find the second order derivative of the function log (log x)
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- Find the second order derivative of the function sin (log x)
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- If y=5 cos x-3 sin x, prove that (d^2y)/(dx^2)+y=0
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- If y=cos ^(-1) x find (d^2y)/(dx^2) in terms of y alone.
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- If y=3 cos (log x)+4 sin (log x) Show that x^2 y2+x y1+y=0
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- If y=ae^(mx)+be^(nx) , show that (d^2y)/(dx^2)-(m+n)dy/dx+mny=0
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- If y=500e^(7x)+600e^(-7x). Show that (d^2y)/(dx^2)=49y
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- If e^y(x+1)=1 , show that (d^2y)/(dx^2)=(dy/dx)^2
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- If y=(tan^(-1)x)^2, show that (x^2+1)^2y2+2x(x^2+1)y1=2 .
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- Verify Rolle's theorem for the function f(x)=x^2+2 in the interval [...
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- Verify Mean Value Theorem for the function f(x)=x^2 in the interval [2...
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- Verify Rolle's Theorem for the function f(x)=x^2+2x-8 , x in [-4,2]
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- If f:[-5,5]toR is a differentiable function and if f'(x) does not vani...
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- Verify mean value theorem for the function f(x)=x^2-4x-3 in the interv...
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- Verify Lagrange 's mean value theorem, if f(x)=x^3-5x^2-3x in the inte...
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- Differentiate w.r.t. x, the following functions: (i) sqrt(3 x+2)+1/(s...
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- Differentiate the following w.r.t. x (i) cos ^(-1)(sin x) (if) tan ^...
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- Find f'(x) if f(x)=(sin x)^(sin x) for all 0ltxltpi
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- For a positive constant a find (dy/dx), where y=a^(t+1/t), and x=(t+1/...
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