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The function f(x)=|x|+|x-1|,is...

The function `f(x)=|x|+|x-1|,is`

A

continuous at x =1, but not differentiable

B

both continuous and differentiable at x = l

C

not continuous at x = 1

D

none of these

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The correct Answer is:
A
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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (2) (MULTIPLE CHOICE QUESTIONS)
  1. If f(x) is defined by: f(x) = {{:((|x^(2)-x|)/(x^(2)-x), (x ne 0,1)),(...

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  2. Let f(x) =|x| + |x-1|, then

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  3. The function f(x)=|x|+|x-1|,is

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  4. Let f(x) = {{:((x^(4) -5x^(2)+4)/(|(x-1)(x-2)|), (x ne 1,2)),(6, x=1),...

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  5. Let f(x) =x-|x-x^(2)|, x in [-1,1].Then the number of points at which ...

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  6. The function f(x) =[x]^(2) -[x^(2)] (where [y] is thegreatest integer ...

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  7. On the interval [-2,2] the function: f(x) = {{:((x+1)e^(-{1/|x|+1/x}...

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  8. Let f(x) = {{:(int(0)^(x) {5+|1-t|dt}, if x gt 2),(5x+1, if x le 2):},...

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  9. The function f(x) =[x] cos{(2x-1)//2} pi denotes the greatest integer...

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  10. The number of points where f(x) =[sin x + cos x] (where [.] denotes th...

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  11. Let f: R to R be any function. Define g : R to R by g(x) = | f(x)|, A...

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  12. If f(x) ={{:(x(e)^(-[1/|x|+1/x]), x ne 0),(0, x=0):}, then f(x) is:

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  13. The function f defined as - f(x) = (sin x^(2))//x for x ne 0 and f(0) ...

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  14. If f(x) = {{:(1, x lt 0),(1 + sinx, 0 le x lt pi//2):} Then at x=0, t...

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  15. For a real number y, let [y] denotes the greatest integer less than o...

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  16. If f(x) = x [sqrt(x) - sqrt(x+1)], then

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  17. The function f(x) = {{:(|x-3|, x ge 1),(x^(2)//4-3x//2 + 13//4, x lt 1...

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  18. The value of the derivative of |x-1| + |x-3| at x=2 is:

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  19. Let [ ] denote the greatest integer function and f(x) = [tan^(2)x] The...

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  20. If f(x) = {{:((|x+2|)/(tan^(-1)(x+2)), x ne -2),(2, x =-2):},

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