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Let f(x) be defined on R such that f(1)=...

Let f(x) be defined on R such that `f(1)=2,f(2)=8 and f(u+v)=f(u)+kuv-2v^(2)` for all `u,v in R` (k is a fixed constant). Then,

A

`f'(x)=8x`

B

`f(x)=8x`

C

`f'(x)=x`

D

None of these

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OBJECTIVE RD SHARMA-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. Let [x] denotes the greatest integer less than or equal to x and f(x)=...

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

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  3. 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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  4. Let f(x) be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x g(x)"For...

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

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

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  7. If f(x+y)=f(x) xx f(y) for all x,y in R and f(5)=2, f'(0)=3, then f'(...

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  8. Let f:RtoR be a function given by f(x+y)=f(x)f(y) for all x,y in R .If...

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

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  10. 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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  11. Let f(x) be a function satisfying f(x+y)=f(x)f(y) for all x,y in R and...

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  12. 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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  13. 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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  14. Let g(x) be the inverse of an invertible function f(x) which is differ...

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  15. Let g(x) be the inverse of the function f(x), and f'(x)=1/(1+x^3) then...

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  16. Let f(x)={{:(,x^(n)"sin "(1)/(x),x ne 0),(,0,x=0):} Then f(x) is conti...

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  17. If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e...

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  18. 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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  19. Let f(0,pi) to R be defined as f(x)={{:(,(1-sinx)/((pi-2x)^(2)).(In si...

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  20. If f(x)=(e^(2x) - (1+4x)^(1//2))/(ln(1-x^2)) for x != 0, then f has

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