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Show that f(x)={(x sin frac{1}{x}, xne0)...

Show that `f(x)={(x sin frac{1}{x}, xne0),(o,x=0):}`
is continuous at x=0

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PROBLEM
  1. If y=cos^(-1)((2cosx-3sinx)/sqrt13), then find dy/dx.

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  2. Examine the continuity of the following functions at indicated points....

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  3. Show that f(x)={(x sin frac{1}{x}, xne0),(o,x=0):} is continuous at x...

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  4. Prove that e^x-2=0 has a solution between 0 and 1.

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  5. So that x^5+x+1=0 for some value of x between -1 and 0.

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  6. Examine continuity and differentiability f(x)={[(1-e^(-x))/x,x!=0],[1,...

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  7. If x=2costheta-cos2theta , y= 2sintheta-sin2theta then find d^(2)y/dx^...

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  8. If y =(sin^(-1) x)^2, prove that (1-x^2)y2 - xy1 - 2 = 0

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  9. Find dy/dx for the following . y=log(2)sqrtsinphi(x).

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  10. Find dy/dx if (x/a)^(2/3) + (y/b)^(2/3) = 1

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  11. Find dy/dx if y = x cot^(-1) (x/y)

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  12. Find dy/dx if (cosx)^(y)=(siny)^(x)

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

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  14. Find dy/dx if e^(3x)In(sin2x)+e^sqrtcosx.

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  15. Differentiate tan^(-1) ((1+sinx)/(1-sinx))^(1/2) w.r.t. log((1+cosx)/(...

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  16. Find dy/dx y=tan^(-1)(xsinalpha-xcosalpha)

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  17. Find dy/dx y = cos^(-1)(1-1/x-1/x^(2))^(1/2)

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  18. Find dy/dx x=cos^(3)t/sqrtcos2t, y=sin^(3)t/sqrt cos2t

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  19. If x =sin t,y = sin 2t then prove that (1-x^2)(d^2y)/(dx^2)- x dy/dx +...

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  20. If y = e^(m cos^(-1) x) (1-x^2)y2-xy1 = m^2y

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