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If f(x)={{:(,x^(2)sin((1)/(x)),x ne 0),(...

If `f(x)={{:(,x^(2)sin((1)/(x)),x ne 0),(,0, x=0):}`, then

A

f and f' are continuous at x=0

B

f is derivable at x=0 and f' is continuous at x=0

C

f is derivable at x=0 and f' is not continuous at x=0

D

f is derivable at x=0

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OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. If f(x)=x^3sgn(x), then

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  2. For a real number y, Let [y] denotes the geatest integer less than ...

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  3. If f(x)={{:(,x^(2)sin((1)/(x)),x ne 0),(,0, x=0):}, then

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  4. The following functions are differentiable on (-1,2)

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  5. If f(x)=sqrt(x+2sqrt(2x-4))+sqrt(x-2sqrt(2x-4)) then the value of 10 f...

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  6. The derivative of f(x)=|x|^(3) at x=0, is

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  7. If f (x) = x (sqrtx+sqrt((x+1)), then

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  8. Write the value of the derivative of f(x)=|x-1|+|x-3|"\ "a t"\ "x=3.

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  9. If f(x)=[x sin pix], then which of the following, is incorrect,

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  10. The function f(x)=1+|sin x|, is

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  11. If f(x)={{:(,1,x lt 0),(,1+sin x,0 le x lt (pi)/(2)):} then derivative...

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  12. Let [x] denotes the greatest integer less than or equal to x and f(x)=...

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  13. A function f : R to R satisfies the equation f(x+y) = f (x) f(y), AA ...

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  14. Let f(x) be defined on R such that f(1)=2,f(2)=8 and f(u+v)=f(u)+kuv-2...

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  15. Let f(x) be a function satisfying f(x+y)=f(x) + f(y) and f(x) = x...

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  16. If f(x)={{:(,ax^(2)-b,|x|lt 1),(,(1)/(|x|),|x| ge1):} is differentiabl...

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  17. If f(x)=(x-x(0)) phi (x) and phi(x) is continuous at x=x(0). Then f'(...

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  18. Let f (x+y) =f (x) f (y) for all x and y, and f(5)=2, f'(0)=3, then f ...

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  19. If f be a function satisfying f(x+y)=f(x)+f(y),AAx,yinR. If f(1) = k, ...

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  20. Let f (x + y) = f(x) f(y) for all x, y, in R, suppose that f(3) = 3...

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