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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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MAXIMUM PUBLICATION-CONTINUITY & DIFFERENTIABILITY-EXAMPLE
  1. Find the derivative of y=x^a+a^x with respect to x.

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

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

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

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  7. Consider a function f:RrarrR defined by f(x)={(a+x,xle2),(b-x,x>2):}...

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  8. Consider a function f:RrarrR defined by f(x)={(a+x,xle2),(b-x,x>2):}...

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  9. Find dy/dx, If x=a(t-sint) , y=a(1+cost)

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  10. Verify Rolle's theorem for the function f(x)=x^2+2 in the interval [...

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  11. Find the relationship between a and b so that the function f defined b...

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  12. Verify mean value theorem for the function f(x)=x^2-4x-3 in the interv...

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  13. Find 'a' and 'b' if the function f(x)={(sinx/x,-2lexle0),(axx2^x,0le...

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  14. Find the relation between 'a' and 'b' if the function f defined by f...

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

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  16. Find the value of a and b such that the function f(x)={(5a,xle0),(asin...

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  17. Find dy/dx , if x=acos^2theta , y=bsin^2theta

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  18. Find the second derivative of the function y=e^xsinx

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  19. Find dy/dx of y^x=x^y

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  20. Find dy/dx of (cosx)^y=(cosy)^x

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