The least upper bound (lub) and greatest lower bound (glb) of the set \(\left\{1 + \frac{(-1)^n}{n} \; ; \; n \in \mathbb{N}\right\}\) are:
For \(f(x) = [x^2 + 1]^{[x + 1]}\), where \([x]\) denotes the greatest integer less than or equal to \(x\), which of the following is not true:
For the function \(f(x) = x^{2/3}(2x + 5)\), if: a) \(x = 0\) is a horizontal tangent b) The curve has no asymptote c) The curve has a cusp at \((0,0)\) d) The curve has no vertical tangent Then:
For the series with \(n^{th}\) term \(x_n = \frac{n}{(n+1)(n+2)}\), the following is true:
The value of \(\lim_{(x,y) \to (0,0)} \frac{x^2y}{x^2 + y^2}\) is:
If \(P(A) = \frac{1}{2}\), \(P(B) = \frac{1}{3}\), and \(P(A \cap B) = \frac{1}{6}\), then \(P(A \cup B)\) is:
A, B, and C are three mutually exclusive and exhaustive events associated with a random experiment. Also, \(P(B) = \frac{3}{2}P(A)\) and \(P(C) = \frac{1}{2}P(B)\), then \(P(A)\) is: