List of top Mathematics Questions on Limits asked in TS EAMCET

If the real valued function \( f(x) = \begin{cases} \frac{\cos 3x - \cos x}{x \sin x}, & \text{if } x < 0 \\ p, & \text{if } x = 0 \\ \frac{\log(1 + q \sin x)}{x}, & \text{if } x > 0 \end{cases} \) is continuous at \( x = 0 \), then \( p + q = \) 

$\lim_{x \to 0} \frac{\sqrt[3]{\cos x} - \sqrt{\cos x}}{\sin^2 x} =$
Let $f:[-1,2] \to \mathbb{R}$ be defined by $f(x) = [x^2-3]$ where $[.]$ denotes greatest integer function, then the number of points of discontinuity for the function $f$ in $(-1,2)$ is
If $[t]$ represents the greatest integer $\leq t$ then the value of $\lim_{x\to 3} \frac{11-[2-x]}{[x+10]}$ is
For $a\neq0$ and $b\neq0$, if the real valued function $f(x) = \frac{\sqrt[4]{625+4x}-5}{\sqrt[4]{625+5bx}-5}$ is continuous at $x=0$, then $f(0) =$
If $\{x\}=x-[x]$ where $[x]$ is the greatest integer $\le x$ and $\lim_{x\to 0^+} \frac{\text{Cos}^{-1}(1-\{x\}^2)\text{Sin}^{-1}(1-\{x\})}{\{x\}-\{x\}^3} = \theta$, then $\tan\theta=$