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Show that the function `f` defined as follows `f(x)={3x-2, 0 < x <=1 , 2x^2 - x ,1< x <=2 , 5x-4, x > 2 is continuous at x=2 , but not differentiable thereat.

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RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  1. Show that f(x)=x^(1//3) is not differentiable at x=0 .

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

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

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

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

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

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

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

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

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

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

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  12. Find the values of a and b , if the function f(x) defined by f(x)={x^2...

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  13. If f(x)=x^2+2x+7 , find f\ '\ (3) .

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  14. Find f\ '\ (2) and f\ '\ (5) when f(x)=x^2+7x+4 .

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  15. For the function f given by f(x)=x^2-6x+8 , prove that f\ '\ (5)=4 .

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  16. Discuss the continuity and differentiability of f(x)={1-x ,\ \ \ \ ...

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  17. Discuss the differentiability of f(x)=|x-1|+|x-2|

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  18. If f(x)={x^2+3x+a ,\ \ \ for\ xlt=1b x+2,\ \ \ \ \ \ \ \ \ \ \ \ \ for...

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  19. Discuss the differentiability of f(x)=|(log)ex| ,x>0

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  20. If f is defined by f(x)=x^2 , find f\ '\ (2) .

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