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Limits and Differentiation Test - 2
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Limits and Differentiation Test - 2

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  • Question 1/8
    1 / -0

    If [x] denotes the integral part of x and f(x) = [x]  then-

    Solutions

    Hence, f(x) is discontinuous at alinteger points 
    ∴Option C. is correct answer.

     

  • Question 2/8
    1 / -0

    A function f(x) is defined as below , x ≠ 0 and f(0) = a f(x) is continuous at x = 0 if a equals.

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  • Question 3/8
    1 / -0

    where [x] denotes the greatest integer less than or equal to x, then in order that f(x) be continuous at x = 0, the value of k is -

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  • Question 4/8
    1 / -0

    The function defined by f(x) =  
    (where [⋅] denotes greatest integer function satisfies)

    Solutions

      

    ∴Option B. is not correct Answer. 

    ∴Option C. is not correct Answer

  • Question 5/8
    1 / -0

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  • Question 6/8
    1 / -0

    Solutions

    Since, f(x) is continuous (There is no need to calculate both limits) 
    Hence, L.H.L = f(2) 
    2 – A = 2 
    ∴Option A is correct Answer.

  • Question 7/8
    1 / -0

    f(x) = [tan–1x] where [ ·] denotes the greatest integer function, is discontinuous at -

    Solutions

    f(x) = [tan–1 x] 
    f(x) will be discontinuous at those points where 
    tan–1x will become integer i.e. 
    tan–1x = 0, ±1, ±2, ±3, ……. 
    x = 0, +tan1, +tan2, +tan3 
    – tan1, –tan2, –tan 3 
    ∴Option C. is correct answer.

  • Question 8/8
    1 / -0

    Let f(x) = Sgn (x) and g(x) = x (x2 –5x + 6). The function f(g (x)) is discontinuous at

    Solutions

      

    f(x) = sgn(x), g(x) = x(x – 3) (x – 2) 
    f(g(x)) = 0 at x = 0, 3, 2

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