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Find the left and right hand derivati...

Find the left and right hand derivative of the following function at given point: `f(x)=ln^2x a t\ x=1`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Proved that: f(x)=[x\ if\ x in Q1-x\ if\ x !in Q\ is continuous onl...

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  2. Find the left and right hand derivative of the following function a...

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  3. Find the left and right hand derivative of the following function a...

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  4. Find the left and right hand derivative of the following function a...

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  5. If f(x) = {{:(|1-4x^(2)|",",0 le x lt 1),([x^(2)-2x]",",1 le x lt 2):}...

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  6. If f(x)={a x+b ,\ xlt=-1a x^3+x+2,\ x > -1 is differentiable for all...

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  7. Find derivative of : f(x)=cos x+|cos x|a t x=pi/2

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  8. The number of points at which the function, f (x)={{:(min {|x|"," x ...

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  9. If incident ray from point (-3, 2) parallel to the axis of parabola...

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  10. Let f be differentiable at x=a\ a n d\ l e t\ f(a)!=0. Evaluate (lim)(...

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  11. Show that the function f(x)={x^msin(1/x)0 ,x!=0,x=0 is differentiab...

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  12. Let f(x)=sgn(x) and g(x)= x(1-x^2), The number of points at which f(...

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  13. Q. f={(x+a if x<0), (x-11 if x>=0) g(x)={(x+1 if x<0),(x-1)^2 if x...

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  14. Discuss the differentiability of f(x)={(x-e)2^(- 2^((1/((e-x))))), x!=...

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  15. Find the domain of f^(prime)(x) if f(x)=[x/(1+|x|)]if\ |x|geq1 , x...

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  16. If f(x) is differentiable at x=a and f^(prime)(a)=1/4dot Find (lim)(h-...

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  17. Let f be a differentiable function satisfying f(x/y)=f(x)-f(y) f...

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  18. Suppose f is a derivable function that satisfies the equation f(x+y...

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  19. If f(x+y)=f(x)dotf(y),\ AAx in R\ a n df(x) is a differentiability...

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  20. If f(x+y)=f(x)+f(y),AAx ,\ y in R then prove that f(k x)=kf(x)for\ AA...

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