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Consider y=tan^-1((sqrt(1+x^2)+1)/x). Pu...

Consider `y=tan^-1((sqrt(1+x^2)+1)/x)`. Put `x= tan theta` and
show that `(sqrt(1+x^2)+1)/x=tan(pi/2-theta/2)`.

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BODY BOOKS PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. If x^3+y^3=3axy. Differentiate through out with respect to x.

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  2. If x^3+y^3=3axy Show that dy/dx=(ay-x^2)/(y^2-ax).

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  3. Consider y=tan^-1((sqrt(1+x^2)+1)/x). Put x= tan theta and show that ...

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  4. Consider y=tan^-1((sqrt(1+x^2)-1)/x). Find dy/dx.

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  5. y=tan x+sec x. Find dy/dx.

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  6. y=tan x+sec x. Prove that (d^2y)/(dx^2)=cosx/((1+sinx)^2.

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  7. If y=sin^-1((sqrt(1+x)+sqrt(1-x))/2) Find dy/dx.

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  8. If y=sin^-1((sqrt(1+x)+sqrt(1-x))/2) Find dy/dx.

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  9. u=(sinx)^(tanx),v=(cosx)^(secx). Find (du)/dxand(dv)/dx.

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  10. u=(sinx)^(tanx),v=(cosx)^(secx) Find dy//dx. if y=(sinx)^(tanx)+(cosx)...

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  11. Given that y=asin nx+b cos nx. Computedy/dx

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  12. Given that y=asin nx+b cos nx. Compute(d^2y)/dx^2

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  13. Given that y=asin nx+b cos nx. Show that(d^2y)/dx^2+n^2y=0.

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  14. Differentiate sin(x^2/3-1) with respect to x.

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  15. Differentiate log{sin(x^2/3-1)} with respect to x.

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  16. Differentiate sqrt(log{sin(x^2/3-1)} with respect to x.

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  17. Consider y=(xsin^-1x)/(sqrt(1-x^2)) Differentiate x. sin^-1x with resp...

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  18. Verify mean value theorem for the function f(x)=(x-2)^2 in [1,4] .

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  19. Find a point on the curve y=(x-2)^2 at which the tangent is parallel t...

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  20. If y=sin(m sin^-1x), Find dy/dx.

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