List of top Mathematics Questions on Limits and Exponential Functions asked in AP EAPCET

The value of $\lim_{x \to \infty} \left(\frac{x+6}{x+1}\right)^{x+4}$ is:

The integral value of \(n\) for which \[ \lim_{x\to 0}\frac{(\cos x-1)(\cos x-e^x)}{x^n} \] is a finite non-zero real number is

Evaluate \(\lim_{x \to 0} \frac{x^2 \log(\cos x)}{\log(1+x^2)}\)

Evaluate \[ \lim_{x\to \infty}x^3\left\{\sqrt{x^2+\sqrt{x^4+1}}-\sqrt2x\right\} \]

If \[ \lim_{x\to 0^+}x^2 \left( \frac{e^{1/x}-e^{-1/x}} {e^{1/x}+e^{-1/x}} \right)=k \] and \[ \lim_{x\to 0^-}x^2 \left( \frac{e^{1/x}-e^{-1/x}} {e^{1/x}+e^{-1/x}} \right)=l, \] then

Evaluate \[ \lim_{x\to 0} \frac{\sqrt{11+|x|-6\sqrt{2+|x|}}} {6-2\sqrt{2+|x|}} \]

The value of \[ \lim_{x\to 0}\left(\frac{e^x-1}{x}\right)^{\frac{1+x-e^x}{x}} \] is

If \(a\gt 0,\ b\gt 0\), then \[ \lim_{n\to\infty} \left( \frac{a+b^{1/n}-1}{a} \right)^n = \] is equal to: