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Establish that g(x)=1-x+absx is continio...

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

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MAXIMUM PUBLICATION-CONTINUITY & DIFFERENTIABILITY-EXAMPLE
  1. Consider f(x)={((x^2-x-6)/(x+2),x ne-2),(-5,x=-2):} Check whether th...

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  2. If f(x)=sin(logx) , prove that x^2y2+xy1+y=0

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

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

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

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  6. Find dy/dx of y=cos^-1frac(1-x^2)((1+x^2)), 0<x<1

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  7. Find dy/dx of y=sin^-1 2xsqrt(1-x^2) (-1)/sqrt2<x<1/sqrt2

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  8. Find dy/dx if x^3+2x^2y+3xy^2+4y^3=5

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  9. Find all points of discontinuity of f where f is defined by f(x)={(2x+...

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  10. If e^(x-y)=x^y then prove that dy/dx=logx/[logex]^2

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  11. Find dy/dx of y=sin^-1(3x-4x^3)+cos^-1(4x^3-3x)

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  12. Find dy/dx of y=tan^-1(sqrt((1-cosx)/(1+cosx)))

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  13. Consider the function f(x)=absx , x in R Draw the graph of f(x)= abs...

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

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

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

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

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

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

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

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