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Let (f(x+y)-f(x))/2=(f(y)-a)/2+x y for a...

Let `(f(x+y)-f(x))/2=(f(y)-a)/2+x y` for all real `xa n dydot` If `f(x)` is differentiable and `f^(prime)(0)` exists for all real permissible value of `a` and is equal to `sqrt(5a-1-a^2)dot` Then (a)`f(x)` is positive for all real `x` (b)`f(x)` is negative for all real `x` (c)`f(x)=0` has real roots (d)Nothing can be said about the sign of `f(x)`

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CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Suppose |[f'(x),f(x)],[f''(x),f'(x)]|=0 is continuously differentiable...

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  2. If f(x)=|[(x-a)^4, (x-a)^3, 1] , [(x-b)^4, (x-b)^3,1] , [(x-c)^4, (x-c...

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  3. Let (f(x+y)-f(x))/2=(f(y)-a)/2+x y for all real xa n dydot If f(x) is ...

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  4. A function f: R -> R satisfies the equation f(x)f(y)-f(x y)=x+yAAx ,y ...

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  5. Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in ...

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  6. Let f(x)=(g(x))/x when x!=0 and f(0)=0. If g(0)=g^(prime)(0)=0and g...

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  7. Let f(x+y)=f(x)+f(y)+2x y-1 for all real xa n dy and f(x) be a differe...

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  8. Let f:(-oo,oo) -> [0,oo) be a continuous function such that f(x+y)=f(x...

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  9. The function f(x) is discontinuous only at x = 0 such that f^(2)(x)=1 ...

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  10. f(x)={(x^2+e^(1/(2-x)))^(-1), x!=2 k ,x=2 is continuous from right at ...

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  11. The derivative of the function represented parametrically as x=2t=|...

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  12. If x=s e ctheta-costhetaa n dy=sec^ntheta-cos^ntheta,p rov et h a t ...

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  13. If f(x)={(1-cos(1-cos x/2))/(2^m x^n)1x=0,x!=0 and f(0)=1 is continuou...

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  14. Find the set of points where the following functions are discontinuous...

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  15. If t(1+x^(2))=x and x^(2)+t^(2)=y then at x = 2, the value of (dy)/(dx...

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  16. A function f: RvecR is defined as f(x)=(lim)(nvecoo)(a x^2+b x+c+e^(n ...

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  17. If x+y=3e^2t h e d/(dx)(x^y)=0forx= e^2 b. e^e c. e d. 2e^2

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  18. xy=( x+y )^n and dy/dx = y/x then n=   1 b.  2 c. 3 d. 4

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  19. If f(x)={(sin(pi/2)(x-[x]),x<5),(5(b-1),x=5),((a b^2|x^2-11 x+24|)/(x-...

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  20. If f(x)={(2cos x -sin2x)/((pi-2x)^2),xlt=pi/2(e^(-cotx)-1)/(8x-4pi),x ...

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