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If f(0)=0" and "underset(xto0)("lim")(f(...

If `f(0)=0" and "underset(xto0)("lim")(f(x))/(x)` exists then this limits is equl to

A

`f'(x)`

B

`f'(0)`

C

`f''(0)`

D

`f(0)`

Text Solution

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The correct Answer is:
B
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MARVEL PUBLICATION-DIFFERENTIATION-MULTIPLE CHOICE QUESTIONS (TEST YOUR GRASP - II : CHAPTER 11)
  1. If f(0)=0" and "underset(xto0)("lim")(f(x))/(x) exists then this limit...

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  2. If x=t*logt" and "y=t^(t)," then: "(dy)/(dx)=

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  3. If 2x=y^(1//n)," then: "x^(2)(y(1))^(2)=

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  4. If y=x^(2)+1" and "u=sqrt(1+x^(2))," then: "(dy)/(dx)=

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  5. If y=sqrt(cos2x)," then: "yy(2)+2y^(2)=

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  6. If x=(t+1)/(t),y=(t-1)/(t)," then: "(dy)/(dx)=

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  7. If d/dx\ ((1+x^2+x^4)/(1+x+x^2)) = ax+b, then (a, b) =

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  8. If cos x =1/sqrt(1+t^(2)), and sin y = t/sqrt(1+t^(2)), then (dy)/(dx)...

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  9. If y=(x^(1/3)-x^(-1/3))then (dy)/(dx) is

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  10. If y=(e^(4logx)-e^(3logx))/(e^(2logx)-e^(logx))," then: "(dy)/(dx)=

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  11. If y=cos^(2)[tan^(-1)sqrt((1-x)/(1+x)))] then dy/dx=

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  12. d/(dx)[sin^(- 1)(x-(4x^3)/27)]= 4x327dx

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  13. (d)/(dx)(sec^(2)x*csc^(2)x)=

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  14. If y=log((1)/(1-x))," then: "(dy)/(dx)-1=

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  15. If y=4^(log2(sinx))+9^(log3(cosx)," then "(log2(log3)y(1)=

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  16. If y=cos((1)/(2)cos^(-1)x)," then "(dx)/(dy)=

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  17. If y=(1+x^(1/4))(1+x^(1/2))(1-x^(1/4)) , then find (dy)/(dx)dot

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  18. If x^(2)=1+cosy," then: "(dy)/(dx)=

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  19. Defferential coefficient of x^(x)w.r.t.x*logx is

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  20. If x=sqrt(y+sqrt(y+sqrt(y+..."to"oo)))," then: "(dy)/(dx)=

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  21. If 3x^(2)+4xy-5y^(2)=0," then: "(dy)/(dx)=

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