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If y=(sin^-1x)^2 , then show that (1-x...

If `y=(sin^-1x)^2` , then show that
`(1-x^2)(d^2y)/(dx^2)-xdy/dx=2`

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BODY BOOKS PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Consider f(x)={(3x-8,xle5),(2k,x>5):} . Find the value of k if f(x) is...

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  2. Find dy/dx , if y=(sinx)^logx , sinx>0

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  3. If y=(sin^-1x)^2 , then show that (1-x^2)(d^2y)/(dx^2)-xdy/dx=2

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  4. Determine the value of k so that the function f(x)={(k(x^2+x+1),x<0)...

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  5. If y=[x+sqrt(x^2+9)]^n , show that dy/dx=(ny)/(sqrt(x^2+9)

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  6. Find dy/dx of x=sqrt(a^(sin^-1t) y=sqrt(a^(cos^-1t)

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  7. Find the values of k so that function f is continuous at the indicated...

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  8. Find dy/dx if y=x^sinx,x>0.

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  9. If y=sin^-1x,then show that (1-x^2)(d^2y)/dx^2-xdy/dx=0

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  10. Check the continuity of the function given by f(x)={(xsinfrac1x,xne0),...

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  11. Verify mean value theorem for the function f(x)=x+frac1x in the interv...

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  12. Find the derivative of y=x^a+a^x with respect to x.

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  13. Find dy/dx if x=acos^3t , y=asin^3t

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  14. If e^y(x+1)=1 , show that (d^2y)/(dx^2)=(dy/dx)^2

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  15. The function f(x)={(5,xle2),(ax+b,2lexle10),(21,xge10):} is continuous...

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  16. Find dy/dx if y=sin(x^sinx)

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  17. If y=ae^(mx)+be^(nx) , show that (d^2y)/(dx^2)-(m+n)dy/dx+mny=0

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  18. Show that the function f(x) defined by f(x)=sin(cosx) is a continuous ...

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  19. If dy/dx=1/(dx/dy) , Show that (d^2y)/(dx^2)=(-(d^2x)/dy^2)/((dx/dy)^3...

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  20. Let y=x^sinx+(sinx)^x . Find dy/dx

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