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Check the continuity of the function giv...

Check the continuity of the function given by `f(x)={(xsinfrac1x,xne0),(1,x=0):}`

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BODY BOOKS PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Find dy/dx if y=x^sinx,x>0.

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Given, y=sqrt(tan^-1x show <be> 2(1+x^2)ydy/dx=1

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  15. Given, y=sqrt(tan^-1x show <be> (1+x^2)y(d^2y)/(dx^2)+(1+x^2)(dy/dx)^2...

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  16. Consider the function f(x)=absx , x in R Show that the function is c...

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

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  18. Check whether h(x)=abs(1-x+absx) is continious at origin.

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  19. Find dy/dx if y=sin(x^3+7).

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  20. Find dy/dx if x=a(t-sin t),y=a(1-cost).

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