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Show that the function f(x)={x \ sin \ 1...

Show that the function `f(x)={x \ sin \ 1/x\ \ \ ,\ \ \ \ w h e n\ x!=0 \ \ \ \ \ \ \ 0, when \ \ \ x=0` is continuous but not differentiable at `x=0` .

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RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  1. Show that the function f(x)=|x-1| for all x in R , is not differentia...

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  2. Discuss the differentiability of f(x)=x|x| at x=0 .

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  3. Show that the function f(x)={x \ sin \ 1/x\ \ \ ,\ \ \ \ w h e n\ x!=0...

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  4. Discuss the differentiability of f(x)={x e-(1/(|x|)+1/x),x!=0x ,x=0a ...

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  5. If f(x) is differentiable at x=a , find (lim)(x->a)(x^2f(a)-a^2\ f(x))...

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  6. For what choice of a and b is the function f(x)={x^2\ \ \ ,\ \ \ xlt=c...

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  7. If f(2)=4 and f^(prime)(2)=1 , then find (lim)(x->2)(x\ f(2)-2f\ (x))/...

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  8. A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all ...

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  9. Show that f(x)=|x-3| is continuous but not differentiable at x=3 .

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  10. Show that f(x)=x^(1//3) is not differentiable at x=0 .

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  11. Show that f(x)={12 x-13 ,\ \ \ if\ xlt=3 \ \ \ \ \ 2x^2+5,\ \ \ \ \ i...

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  12. Show that the function f defined as follows f(x)={3x-2, 0 < x <=1 , 2x...

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  13. Discuss the continuity and differentiability of the function f(x)=|...

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  14. Find whether the following function is differentiable at x = 1 and x...

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  15. Show that the function f(x)={x^msin(1/x), x=0 ,0 ,\ \ \ x!=0 ,\ \ \ \...

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  16. Show that the function f(x)={x^msin(1/x),\ \ \ x!=0 , 0\ \ x=0 is d...

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  17. Show that the function f(x)={x^msin(1/x),\ \ \ x!=0 0,\ \ \ \ \ \ \ \...

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  18. Find the values of a and b so that the function f(x)={x^2+3x+a ,\ \ if...

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  19. Show that the function f(x)={|2x-3|\ [x],\ \ xgeq1; \ \ \ \ \ \ \ \ ...

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  20. If f(x)={a x^2-b ,\ \ \ if\ |x|<1 1/(|x|),\ \ \ \ \ \ \ \ \ \ \ \ if\ ...

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