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Using mathematical induction prove that ...

Using mathematical induction prove that `d/(d x)(x^n)=n x^(n-1)` for all positive integers `n`.

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BODY BOOKS PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. If y=sin(m sin^-1x), Hence prove that (1-x^2)(d^2y)/dx^2-xdy/dx+m^2y=0...

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  2. Verify Lagrange 's mean value theorem, if f(x)=x^3-5x^2-3x in the inte...

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  3. Using mathematical induction prove that d/(d x)(x^n)=n x^(n-1) for all...

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  4. Choose the correct answer from the bracket. If x=sin t and y= cos t, t...

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  5. Find the value of k such that the function f(x) defined by f(x)={(kx-1...

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  6. If y^x=e^(y-x), prove that dy/dx=(1+logy)^2/logy.

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  7. Find the value of a such that the function f(x) defined by f(x)={(ax+3...

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  8. If x=acos^3theta and y=asin^3theta. Prove that 1+(dy/dx)^2=sec^2theta.

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  9. Choose the correct answer from the bracket. If x=at^2,y=2at, then the ...

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  10. Is the function defined by f(x)={(x+3,ifxle1),(x-3,ifx>1):} a continuo...

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  11. Find dy/dx, if y=tan^-1((cosx-sinx)/(cosx+sinx))

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  12. If x^(2)+2xy+2y^(2)=1, then (dy)/(dx) at the point where y=1 is equal ...

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  13. Find the relationship between a and b so that the function f defined b...

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  14. If x^yy^x=16, then find dy/dx at (2,2).

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  15. Verify Lagranges' Mean value theorem for the function f(x)=2x^2-10x+29...

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  16. If f(x)=log[e^(x)((3-x)/(3+x))^(1//3)] then f'(1) is equal to a)(3)/(4...

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  17. Verify Rolle's theorem for the function f(x)=sin3x on [0,pi/3].

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  18. Let y=(x+sqrt(1+x^2))^m Find dy/dx.

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  19. Let y=(x+sqrt(1+x^2))^m Show that (1+x^2)(d^2y)/dx^2+xdy/dx-m^2y=0.

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  20. Find dy/dx if sinx+cosy=xy

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