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Mathematics Test - 16
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  • Question 1/10
    5 / -1
    Which of the following functions is not continuous at the origin?
  • Question 2/10
    5 / -1
    If a function f(x) = \(\begin{Bmatrix} \rm 3x + 2, x \geq1\\ \rm 5, \;\;\;\;\;\;\;\;x<1 \end{Bmatrix}\), then the function at x = 1
  • Question 3/10
    5 / -1
    What is the derivative of tan-1 x with respect to cot-1 x ?
  • Question 4/10
    5 / -1

    The value of ε in the Lagrange's mean value theorem of f(b) - f(a) = (b - a) f'(ε) for f(x) = Ax2 + Bx + C in (a, b) is

  • Question 5/10
    5 / -1
    If \(\text{f(x)} = \left\{ \begin{matrix} \dfrac { \log \ x}{x - 1} & \text{if} \ x \ne 1 \\\ K & \text{if} \ x = 1 \end{matrix} \right.\) is continuous at x = 1, then the value of K is
  • Question 6/10
    5 / -1
    Let f be a continuous on [1, 5] and differentiable in (1, 5) if f(1) = - 3 and f'(x) ≥ 9 for all x ∈ (1, 5) then which of the following is correct?
  • Question 7/10
    5 / -1
    If f(x) = x|x| and g(x) = sin x then  gof(x) then at x = 0
  • Question 8/10
    5 / -1
    The function f(x) is defined by \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{\left| x \right|}}{x}}\\ {0,} \end{array}\begin{array}{*{20}{c}} {,x \ne 0}\\ {x = 0} \end{array}} \right.\) then, at x = 0 it is
  • Question 9/10
    5 / -1

    If \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {1 + x}&{if\;x < 0}\\ {\left( {1 - x} \right)\left( {px + q} \right)}&{if\;x \ge 0} \end{array}} \right.\)

    Satisfy the assumption of Rolle’s theorem in the interval [-1, 1], then ordered pair (p, q) is
  • Question 10/10
    5 / -1
    At how many points is the function f(x) = [x] discontinuous?
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