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Let [x] denotes the greatest integer les...

Let [x] denotes the greatest integer less than or equal to x and `f(x)=[tan^(2)x]`. Then

A

`underset(x to 0)f(x)` does not exist

B

f(x) is continuous at x=0

C

f(x) is not continuous at x=0

D

f'(0)=1

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OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. The function f(x)=1+|sin x|, is

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

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

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

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

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

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

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

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

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  12. Let f(x+y)=f(x)+f(y) and f(x)=x^2g(x)AA x,y in R where g(x) is continu...

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  13. Let f(x+y)=f(x)f(y) for all x, y epsilon R and f(x)=1+x phi (x) l n 2 ...

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  14. Let f(x+y)=f(x) f(y) and f(x)=1+(sin 2x)g(x) where g(x) is continuous....

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  15. Let f(x+y)=f(x) f(y) and f(x)=1+(sin 2x)g(x) where g(x) is continuous....

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  16. Let g(x) be the inverse of an invertible function f(x) which is differ...

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  17. Let g(x) be the inverse of f(x) and f'(x)=1/(1+x^(3)).Find g'(x) in te...

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  18. Let f(x)={{:(,x^(n)sin\ (1)/(x),x ne 0),(,0,x=0):} Then f(x) is contin...

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  19. If for a continuous function f,f(0)=f(1)=0,f'(1)=2 and y(x)=f(e^(x))e^...

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  20. Let f(x) be a function such that f(x+y)=f(x)+f(y) and f(x)=sin x g(x)...

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