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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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V PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Find (dy/dx), if y=sin ^(-1) x+sin ^(-1) sqrt(1-x^2),-1 le x le 1

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  2. if x sqrt(1+y)+ysqrt(1+x)=0 prove that (dy/dx)=-1/(1+x)^2

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  3. if (x-a)^2+(y-b)^2=c^2, for some c>0 prove that [1+(dy/dx)^2]^(3/2) /(...

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  4. If cos y=x cos (a+y) prove that (dy/dx)=(cos ^2(a+y))/sina

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  5. If x=a(cos t+t sin t) and y=a(sin t-t cos t), find (d^2y)/(dx^2)

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

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  7. Using the fact that sin (A+B)=sin A cos B+cos A sin B and the techniqu...

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  8. "All continuous function are not differentiable." Justify your answe...

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  9. If y=|[f(x), g(x), h(x)],[ l, m , n],[ a , b , c]| prove that (dy/...

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  10. If y=e^(acos^-1x) , then show that (1-x^2)y2-xy1-a^2y=0

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  11. Let y=(x+sqrt(1+x^2))^m i) Find (dy/dx) ii) Show that (1+x^2) (d^2 y...

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  12. Let y=tan ^(-1)((1-cos x)/(sin x)) i) Express 1-cos x and sinx in ter...

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  13. If x y=a x^2+b/x, prove that x^2 y2+2(x (dy/dx)-y)=0

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  14. Establish that g(x)=1-x+absx is continious at origin.

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  15. a) Find (dy/dx) if i) y=sin (x^3+7) ii) x=a(t-sin t), y=a(1-cos t) ...

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  16. Discuss the continuity of the function f(x)={(sin x/x , if , x<0),( ...

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  17. Find the point of discontinuities of the function. (x+1)/(12 x^2+7 x-1...

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  18. Consider f(x)={(3x-8,xle5),(2k,x>5):} . Find the value of k if f(x) is...

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  19. Find the point of discontinuity, if any of the following functions f...

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  20. Find the value of m, if any, so that the function h(x)={(m(x^2-2 x) , ...

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