List of top Mathematics Questions on Limits asked in AP EAPCET

The value of \[ \lim_{x\to0}\frac{\sin5x-5\sin x}{x^3} \] is:

If \(n\gt 0\) and \[ \lim_{x\to 0}\frac{((a-n)nx-\tan x)\sin nx}{x^2}=0, \] then minimum value of \(a\) is

Evaluate \[ \lim_{x\to \frac{\pi}{6}} \frac{3\sin x-\sqrt{3}\cos x}{6x-\pi} \]

Evaluate \[ \lim_{n\to\infty}\sqrt{2} \left[ \frac{(2+\sqrt{2})^n+(2-\sqrt{2})^n} {(2+\sqrt{2})^n-(2-\sqrt{2})^n} \right] \]

If \(a\gt 0\), \([\,]\) denotes greatest integer function and \[ \lim_{x\to a} \left( \frac{[x]^3}{a}-\left[\frac{x}{a}\right]^3 \right)=k, \] \[ \lim_{x\to a} \left( \frac{[x]^5}{a}-\left[\frac{x}{a}\right]^3 \right)=l, \] then

Evaluate \[ \lim_{n\to\infty}\frac{A+e^{nx}}{x+Ae^{nx}} \]

Evaluate \[ \lim_{x\to 0}\frac{3|x|-x}{|x|-2x} - \lim_{x\to 0}\frac{\log(1+x^3)}{\sin^3 x} \]

Evaluate \[ \lim_{x\to -\infty}\log_e(\cosh x)+x \]

If \(a,b,c\) are three distinct real numbers and \[ \lim_{x\to \infty} \frac{(b-c)x^2+(c-a)x+(a-b)} {(a-b)x^2+(b-c)x+(c-a)} = \frac{1}{2} \] then \(a+2c=\)

If \(l,m\;(l\lt m)\) are roots of \(ax^2+bx+c=0\), then \[ \lim_{x\to \alpha}\frac{|ax^2+bx+c|}{ax^2+bx+c}= \]

Let \[ f(x)= \begin{cases} \dfrac{1}{|x|}, & \text{for } |x|\gt 1 \\[0.3cm] ax^2+b, & \text{for } |x|\leq1 \end{cases} \] If \[ \lim_{x\to1}f(x) \quad \text{and} \quad \lim_{x\to-1}f(x) \] exist, then the possible values of \(a\) and \(b\) are

If \([\,]\) denotes greatest integer function, then \[ \lim_{x\to -\frac{3}{5}}\frac{1}{x}\left[\frac{-1}{x}\right] \] is