List of top Mathematics Questions on Calculus asked in KEAM

The cubic polynomial \( 2x^3 - 3x^2 - 36x + 28 \) is increasing in the range of \( x \). Find the interval where the function is increasing.

Evaluate the limit: \[ \lim_{x \to \infty} \frac{\sqrt{\cos^2 x + 3} - \sqrt{\cos^2 x + \sin x + 3}}{x} \]

Let \(f(x)=\begin{cases}1-5x,&\text{if } x<-2\\x^{2}-2x,&\text{if } -2\le x\le1\\-1+2x,&\text{if } x>1\end{cases}\). Then the value of \(f(-1)\) is equal to

Let \( f_n(x) \) be the \(n^{\text{th}}\) derivative of \( f(x) \). The least value of \( n \) such that \[ f_n(x) = f_{n+1}(x) \] where \[ f(x) = x^2 + e^x \] is: