Limits (p-1) Maths (commerce) - Limits (p-1)

$\lim _{x \rightarrow 0}\left[\frac{\log (1+9 x)}{x}\right]$

$\lim _{x \rightarrow 0}\left(1+\frac{x}{5}\right)^{\frac{1}{x}}$

$\lim _{x \rightarrow 0}\left[\frac{5^x-1}{x}\right]$

$\lim _{x \rightarrow 4}\left[\frac{3-\sqrt{5+x}}{1-\sqrt{5-x}}\right]$

Evaluate the limit of the function if exist at $x=1$ where,
$
f(x)= \begin{cases}7-4 x & x<1 \\ x^2+2 & x \geq 1\end{cases}
$

$\lim _{x \rightarrow 0}\left[\frac{\log 100+\log (0.01+x)}{x}\right]$

$\lim _{x \rightarrow 0}\left[\frac{a^{4 x}-1}{b^{2 x}-1}\right]$

$\lim _{x \rightarrow 0}\left[\frac{\left(5^x-1\right)^2}{x \cdot \log (1+x)}\right]$

$\lim _{x \rightarrow 0}\left[\frac{a^{3 x}-a^{2 x}-a^x+1}{x^2}\right]$

$\lim _{x \rightarrow 0}\left[\frac{\log (4-x)-\log (4+x)}{x}\right]$

$\lim _{x \rightarrow 0}\left[\frac{x\left(6^x-3^x\right)}{\left(2^x-1\right) \cdot \log (1+x)}\right]$

$\lim _{x \rightarrow 0} \frac{(1-x)^5-1}{(1-x)^3-1}$

$\lim _{x \rightarrow 0}\left[\frac{(49)^x-2(35)^x+(25)^x}{x^2}\right]$

$\lim _{x \rightarrow 0}\left[\frac{\left(2^x-1\right)^2}{\left(3^x-1\right) \cdot \log (1+x)}\right]$

$\lim _{x \rightarrow 0}\left[\frac{\log (2+x)-\log (2-x)}{x}\right]$

$\lim _{x \rightarrow 2}\left[\frac{x^3-8}{\sqrt{x+2}-\sqrt{3 x-2}}\right]$

$\lim _{x \rightarrow 0}\left[\frac{\sqrt{1+x^2}-\sqrt{1+x}}{\sqrt{1+x^3}-\sqrt{1+x}}\right]$

$\lim _{x \rightarrow a}\left[\frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}}\right]$

$\lim _{x \rightarrow 3}\left[\frac{x-3}{\sqrt{x-2}-\sqrt{4-x}}\right]$

$\lim _{x \rightarrow 0}\left[\frac{a^{3 x}-b^{2 x}}{\log (1+4 x)}\right]$

$\lim _{x \rightarrow 0}\left[\frac{\log (3-x)-\log (3+x)}{x}\right]$