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A function f(x) is defined as follows : ...

A function f(x) is defined as follows :
`f(x)={(x^(2)"sin"(1)/(x)", if "x!=0),(0", if "x=0):}`
show that f(x) is differentiable at x=0.

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ARIHANT PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -(PART II) QUESTION FOR PRACTICE (1 MARK)
  1. Prove that the function f gives by f(x)=|x-1|x in R is not differentia...

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  2. Show that the function f(x)=|x-1|+|x+1| AA x in R is not differentia...

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  3. A function f(x) is defined as follows : f(x)={(x^(2)"sin"(1)/(x)", i...

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  4. Let f(x)=x|x|,AA x in R. Discuss the derivability of f(x) at x=0.

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  5. Examine the differentiability of the function f defined by f(x)={{:(2x...

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  6. Discuss the continuity and differentiability of function f(x)=|x|+|x-1...

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  7. Prove that the greatest interger function defined by f(x)=[x],0ltxlt3 ...

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  8. If f(x)=|cos x-sinx| then find f ' ((pi)/(6))

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  9. Differentiate sqrt(tan sqrt(x)) w.r.t. x.

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  10. Differentiate cos x^(3)* sin^(2)(x^(5)) w.r.t.x.

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  11. If y=sin[sqrt(sin sqrt(x))], then find (dy)/(dx).

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  12. If y=xtan x+secx, then find the value of (dy)/(dx) at x=(pi)/(4).

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  13. If y=sin^(3)sqrt(ax^(2)+bx+c) then find (dy)/(dx)

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  14. If y=[x+sqrt(x^(2)+a^(2))]^(n), then prove that (dy)/(dx)=(ny)/(sqrt(x...

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  15. If y=sqrt((1-sin2x)/(1+sin2x)), then show that (dy)/(dx)+sec^(2)((pi)/...

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  16. Prove that y=tan(x+y), then (dy)/(dx)=(1+y^(2))/(-y^(2))

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  17. Differentiate from definition (x^(2)+3x+5)

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  18. Differentiate from definition e^(sinx)

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  19. Differentiate from definition sqrt(cosx)

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  20. Differentiate from definition (sinx)/(x)

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