List of top Mathematics Questions on Differential Calculus asked in IIT JAM MS

Let \(f:\mathbb{R}\to\mathbb{R}\) be the function defined by \(f(x)=3e^x\cos 2x\). If \(p(x)=ax^3+bx^2+cx+d\) is the third degree Taylor polynomial of \(f\) at \(x=0\), then \(|a|+|b|+|c|+|d|\) equals (in integer).

Let \(h:\mathbb{R}\to\mathbb{R}\) and \(g:\mathbb{R}\to\mathbb{R}\) be two bounded functions. Define the function \(f:\mathbb{R}\to\mathbb{R}\) by

Let \(f:\mathbb{R}\setminus\{0\}\to \mathbb{R}\) and \(g:\mathbb{R}\setminus\{0\}\to \mathbb{R}\) be two bounded and differentiable functions. Define \(F:\mathbb{R}^2\to \mathbb{R}\) by

Let \(g:\mathbb{R}\to\mathbb{R}\) be a function defined by