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If for a continuous function `f,f(0)=f(1)=0,f'(1)=2 and y(x)=f(e^(x))e^(f(x)),` then y'(0) is equal to

A

1

B

2

C

0

D

None of these

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OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise
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  3. If f(x)={{:(,ax^(2)-b,|x|lt 1),(,(1)/(|x|),|x| ge1):} is differentiabl...

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

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

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  8. 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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  9. 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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  10. 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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  11. 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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  12. Let g(x) be the inverse of an invertible function f(x) which is differ...

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

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  15. 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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  16. 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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  17. Let f(0,pi) to R be defined as f(x)={{:(,(1-sinx)/((pi-2x)^(2)).(In si...

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

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  19. Let f(x)={{:(,(ex^(2)-(2)/(pi)sin^(-1)sqrt(1-x))/(In(1+sqrtx)),x in (0...

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  20. Let f(x)={{:(,x^(3),x lt 1),(,ax^(2)+bx+c,:x ge 1):}. If f''(1) exists...

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