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Let a function f:RtoR satisfy the equati...

Let a function `f:RtoR` satisfy the equation `f(x+y)=f(x)=f(Y)AAx, yepsilonR`. If the function f(x) is continuous at x=0, then

A

`f'(x)=0" for all "x in R`

B

`f'(0)ltf'(1)`

C

`f'(x)" does not exist"`

D

none of these

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-DIFFERENTIATION-Chapter Test
  1. If y=sin^(-1){(5x+12 sqrt(1-x^(2)))/(13)}, find (dy)/(dx).

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  2. If f(x)=cos^(-1){(1-(log(e)x)^(2))/(1+(log(e)x)^(2))}, then f'( e )

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  3. y=sin^(-1)[sqrt(x-ax)-sqrt(a-ax)]

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  4. Let f(x)=(x^3+2)^(30) If f^n (x) is a polynomial of degree 20 where f^...

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  5. If f(x)=cos^(2)x+cos^(2)(x+(pi)/(3))+sinxsin(x+(pi)/(3)) and g((5)/(4)...

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  6. If f(x)=10cosx+(13+2x)sinx then f''(x)+f(x)=

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  7. Let a function f:RtoR satisfy the equation f(x+y)=f(x)=f(Y)AAx, yepsil...

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  8. If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2...

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  9. If f'(x)=arc tan((x^(x)-x^(-x))/(2)), then f'(1) is equal to

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  10. Let f(x)=2^(2x-1)" and "g(x)=-2^(x)+2xlog2. Then the set of points sat...

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  11. If y=logu|cos4x|+|sinx|,where u=sec2x find (dy)/(dx) at x=-pi/6

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  12. If f(4)= 4, f'(4) =1 then lim(x to 4) 2((2-sqrtf(x))/ (2 - sqrtx)) is ...

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  13. if 2x^2-3xy+y^2+x+2y-8=0 then (dy)/(dx)

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  14. If y=log{((1+x)/(1-x))^(1//4)}-(1)/(2)tan^(-1)x," then "(dy)/(dx)=

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  15. If x=costheta,y=sin5theta," then "(1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx...

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  16. If f : R - R is an even function which is twice differentiable on R an...

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  17. Observe the following statements: "I. If "f(x)=ax^(41)+bx^(-40)," ...

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  18. If x=e^tsint,y=e^tcost then (d^2y)/(dx^2) at x=pi is

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  19. The value of (dy)/(dx) at x=(pi)/(2), where y is given by y=x^(sinx)...

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  20. If 2^(x)+2^(y)=2^(x+y) then (dy)/(dx)is equal to

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