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

Show that the function `f(x)={|2x-3|\ [x],\ \ xgeq1; ` `\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ sin((pix)/2),\ \ \ x<1` is continuous at `x=1` .

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RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  1. Show that the function f(x)={x^msin(1/x),\ \ \ x!=0 0,\ \ \ \ \ \ \ \...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. If f is defined by f(x)=x^2-4x+7 , find f\ '\ (x)

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  15. find the derivative of the function f given by f(x)=2x^3-9x^2+12 x+9

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  16. If for the function "Phi"(x)=lambdax^2+7x-4,\ \ "Phiprime^"(5)=97 , fi...

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  17. If f(x)=x^3+7x^2+8x-9 , find f\ '\ (4) .

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  18. Find the derivative of the function f defined by f(x)=m x+c at x=0 ...

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  19. Examine the differentiability of the function f defined by f(x)={2x+...

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  20. Write an example of a function which is everywhere continuous but f...

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