CUET Mathematics 2025 16 May Shift 1 PYQs

Let

$f(x)=\begin{cases} |x|+3 & \text{if } x\le -3 \\ -2x & \text{if } -3<x<3 \\ 6x+2 & \text{if } x\ge 3 \end{cases}$

Then, which of the following is true?

The function $f(x) = [x]$, where $[x]$ denotes the greatest integer function, is continuous at $x =$

(A) 2.9

(B) 5

(C) -3

(D) 6.5

Choose the correct answer from the options given below:

If $y = t - \frac{1}{t}$ and $x = t + \frac{1}{t}$, then $\frac{dy}{dx}$ is equal to