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

If `y=sin^(-1)x`, show that `(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0`.

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Verified by Experts

`y=sin^-1x`
`frac{dy}{dx}=frac{1}{sqrt(1-x^2)}`
`frac{d^2y}{dx^2}=``frac{-1}{2}(1-x^2)^(frac{-1}{2}1)``(-2x)`
`frac{d^2y}{dx^2}=(1-x^2)^-frac{-3}{2}(x)`
`frac{d^2y}{dx^2}=frac{x}{1-x^2}frac{1}{sqrt(1-x^2)}`
`frac{d^2y}{dx^2}=frac{x}{1-x^2}frac{dx}{dy}`
`(1-x^2)frac{d^2y}{dx^2}-xfrac{dy}{dx}=0`
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NCERT-CONTINUITY AND DIFFERENTIABILITY-SOLVED EXAMPLES
  1. Verify the Mean Value Theorm for f(x)=x^2 in the interval [2,4].

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  2. If y=3e^(2x)+2e^(3x). Prove that (d^2y)/(dx^2)-5(dy)/(dx)+6y=0.

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  3. If y=sin^(-1)x, show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0.

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  4. Find all the points of discontinuity of the function f defined byf(x)=...

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  5. Discuss the continuity of the function f defined by f(x)={(x+2,"if",x...

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  6. Discuss the continuity of the function f given by f(x)={x , ifxgeq0x^2...

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  7. Discuss the continuity of the function defined byf(x)={x+2, ifx<0-x+2,...

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  8. Find all the points of discontinuity of the greatest integer function...

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  9. Show that every polynomial function is continuous.

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  10. Discuss the continuity of sine function.

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  11. Prove that every rational function is continuous.

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  12. Show that the function defined by f(x) = sin(x^2)is a continuous func...

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  13. Prove that the function defined by f(x) = t a n xis a continuous func...

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  14. Examine whether the function f given by f(x)=x^2 is continuous at x =...

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  15. Discuss the continuity of the function f given by f(x) = |x| at x = 0.

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  16. Check the continuity of the function f given by f(x) = 2x + 3 at x = ...

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  17. Prove that the identity function on real numbers given by f(x) = x is...

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  18. Is the function defined by f(x) = |x|, a continuous function?

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  19. Show that the function f given by f(x)={x^3+3ifx!=0 ;1ifx=0 is not ...

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  20. Check the points where the constant function f(x) = kis continuous.

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