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If f is an even function such that `lim_(hrarr0)(f(h)-f(0))/h` has some finite non-zero value, then

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CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. In the function f(x)=[(x-2)^3/a]sin(x-2)+acos(x-2), (where [.] denote...

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  2. Let g(x)=[(3x^2-4sqrtx+1, x<1),(ax+b, x>=1)) If g(x) is continuous and...

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  3. If f is an even function such that lim(hrarr0)(f(h)-f(0))/h has some f...

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  4. Solve 2[x]=x+{x},where [.] and {} denote the greatest integer function...

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  5. Number of points where f(x)=|x sgn(1-x^2)| is non-differentiable is...

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  6. Let f(x) be differentiable for real such that f'(x)lt0" on "(-4,6) a...

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  7. Number of point where function f(x) defined as f:[0,2pi] rarrR,f(x)={{...

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  8. The differential coefficient of sin^(-1)((4sin2x+3cos2x)/5)with respec...

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  9. Let g(x)=f(x)sinx ,w h e r ef(x) is a twice differentiable function on...

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  10. If f(x)=(log)x(lnx),t h e nf^(prime)(x) at x=e is equal to 1/e (b) e ...

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  11. If f(x-y)=f(x).g(y)-f(y).g(x) and g(x-y)=g(x).g(y)+f(x).f(y) for all x...

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  12. If x e^(x y)-y=sin^2x then (dy)/(dx)a tx=0 is a. 0 b. 1 c. -1 d. none ...

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  13. The right hand derivative of f(x) = [x] tanpix at x = 7 is (where [.] ...

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  14. If y=(x^2)/2+1/2xsqrt(x^2+1)+1/2(log)esqrt(x+sqrt(x^2+1)) , prove that...

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  15. Let f, g and h are differentiable functions. If f(0) = 1; g(0) = 2; ...

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

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  17. If y=x^((log x)^(log(log,x)))," then "(dy)/(dx) is

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  18. d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2s...

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  19. Let g(x)=e^(f(x)) and f(x+1)=x+f(x) AA x in R. If n in I^(+)", then"(g...

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  20. Let g(x) be the inverse of f(x) and f'(x)=1/(1+x^3). Then find g'(x) i...

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