Consider that for a supervised learning task, the objective function being minimized is \(f_w(x) = wx\), where \(x \in \mathbb{R}\…

The value of \(\displaystyle\sum_{i=0}^{\infty}\sum_{j=1}^{\infty} 2^{-i}\,3^{-j}\) is ________. (Answer in integer)

Let \( f(x) = \frac{e^x - e^{-x}}{2}, \, x \in \mathbb{R} \). Let \( f^{(k)}(a) \) denote the \( k^{th} \) derivative of \( f \) e…

Consider two functions \( f: \mathbb{R} \to \mathbb{R} \) and \( g: \mathbb{R} \to (1, \infty) \). Both functions are differentiab…

Evaluate the following limit: \[ \lim_{t \to \infty} \sqrt{t^2 + t - t} \]

Consider the function \( f(x) = \frac{x^3}{3} + \frac{7}{2}x^2 + 10x + \frac{133}{2} \), \( x \in [-8, 0] \). Which of the followi…