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Consider f(x)=[(2(sinx-sinx-sin^3x))+|s...

Consider `f(x)=[(2(sinx-sinx-sin^3x))+|sinx-sin^3 x|)/(2(sinx-sin^3 x)-|sinx-sin^3x|], x != pi/2` for `x in (0,pi), f(pi/2) = 3` where [ ] denotes the greatest integer function then,

A

f is continuous and differentiable at `x = pi//2`

B

f is continuous but not differentiable at `x = pi//2`

C

f is neither continuous nor differentiable at `x = pi//2`

D

None of the above

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The correct Answer is:
A
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
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  7. Given f(x) = (e^(x)-cos 2x - x)/(x^(2)),"for x" in R-{0} g(x) = {{:(f(...

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  8. The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} cannot be m...

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  9. The graph of function f contains the point P(1, 2) and Q(s, r). The e...

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  10. Consider f(x)=[(2(sinx-sinx-sin^3x))+|sinx-sin^3 x|)/(2(sinx-sin^3 x)...

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  11. If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0, then

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  12. Let f(x) = max. {|x^2 - 2 |x||,|x|} and g(x) = min. {|x^2 - 2|x||, |x|...

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

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  14. Let f(x) be continuous and differentiable function for all reals and f...

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  15. Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) ...

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  16. If f(x) = {{:(b([x]^(2)+[x])+1",","for",x ge -1),(sin(pi(x+a))",","for...

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  17. If both f(x) & g(x) are differentiable functions at x=x0then the fun...

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  18. Number of points of non-differentiability of the function g(x) = [x^2...

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  19. If f(x) = ({x}g(x))/({x}g(x)) is a periodic function with period (1)/(...

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  20. If f((x)/(y))=(f(x))/(f(y)) for all x, y in R, y ne 0 and f'(x) exists...

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