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Show that the function f(x)={ x^2sin(1/x...

Show that the function f(x)={ `x^2sin(1/x) ,` when `x !=0` and `0` when `x=0` } is differentiable at x=0.

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RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  1. For what choice of a and b is the function f(x)={x^2,xlt=c and a x+...

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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^2sin(1/x) , when x !=0 and 0 when x=0 ...

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  4. If f(2)=2a n df^(prime)(2)=1, then find (lim)(xvec2)(xf(2)-2f(x))/(x-2...

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  5. If sin^-1 x+sin^-1 y+sin^-1 z=(3pi)/2, then find the value of x^2+y^2+...

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  6. Show that f(x)=|x| is not differentiable at x=0 .

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  7. Show that the function f(x)={x-1\ \ \ ,\ \ \ if\ x<2 \ \ \ \ \ \ \ ...

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  8. Show that the function f(x)={((x^2sin(1/x),if,x!=0),(0,if,x=0)) is dif...

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  9. Show that f(x)=x^2 is differentiable at x=1 and find f^(prime)(1) .

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  10. Show that the function f(x)=|x-1| for all x in R , is not differentia...

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

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

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

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

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

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

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

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

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

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

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