Mathematics Tes...

Which of the following functions is not continuous at the origin?

If a function f(x) = \(\begin{Bmatrix} \rm 3x + 2, x \geq1\\ \rm 5, \;\;\;\;\;\;\;\;x<1 \end{Bmatrix}\), then the function at x = 1

What is the derivative of tan^-1 x with respect to cot^-1 x ?

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

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

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?

If f(x) = x|x| and g(x) = sin x then  gof(x) then at x = 0

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

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

At how many points is the function f(x) = [x] discontinuous?