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Show that the function f(x)={x^msin(1...

Show that the function `f(x)={x^msin(1/x)0` `,x!=0,x=0` is differentiable at `x=0,ifm >1` continuous but not differentiable at `x=0,if0

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. If incident ray from point (-3, 2) parallel to the axis of parabola...

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

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

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

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

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

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

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

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

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

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  12. 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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  13. Discuss the differentiability of f(x)={(sinx^2)/x ,x!=0 0,x=0a tx=0

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  14. Discuss the differentiability of f(x)=|x|||x-1|dot

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  15. Discuss the differentiability of f(x)=m a xi mu m{2sinx ,1-cosx}AAx...

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  16. Discuss the differentiability of f(x)=e^(-|x|)

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  17. If f(x)={x ,\ xlt=1x^2+b x+c ,\ x >1 , then find the values of b...

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  18. Find the values of aa n db if f(x)={a+sin^(-1)(x+b),xgeq1x ,x<1 is di...

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

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  20. Find x where f(x)=m a xi mu m{sqrt(x(2-x)),2-x} is non-differentiable.

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