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How to find $\lim\limits_{x\to0}\frac{e^x-1-x}{x^2}$ without using l'Hopital's rule nor any series expansion?

how can I use taylor series to approximate these two functions?

$\lim_{x\to0} \frac{x-\sin x}{x-\tan x}$ without using L'Hopital

Calculating the limit $\lim_{x \to 0} \frac{1 + \sin x - \cos x + \ln(1-x)}{x^3}$ without using l'Hospital rule or Taylor series

Evaluate $\lim_{x \to 0} \frac{\ln\left[\frac{(1-3x)(1+x)^3}{(1+3x)(1-x)^3}\right]}{x^3}$ without L'Hôpital/Taylor/differentiation/integration

How to find $\lim_{n\to \infty} \frac{\log(n)}{n}$ without L'Hospital's rule? [duplicate]

What's wrong with l'Hopital's rule?

Evaluation of $\lim\limits_{x\rightarrow0} \frac{\tan(x)-x}{x^3}$

Determine $\lim_{x \to 0}{\frac{x-\sin{x}}{x^3}}=\frac{1}{6}$, without L'Hospital or Taylor

Show $\lim_{h\to 0} \frac{(a^h-1)}{h}$ exists without l'Hôpital or even referencing $e$ or natural log

Find $\lim_\limits{x\to -\infty}{\frac{\ln\left(1+3^x\right)}{\ln\left(1+2^x\right)}}$

How can I approximate these two functions?

Are all limits solvable without L'Hôpital Rule or Series Expansion

How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?

New posts in limits-without-lhopital

Are there any situations in which L'Hopital's Rule WILL NOT work?

Does the limit : $\lim _{x\to \infty }\frac{\ln x^{\frac{1}{3}}}{\sin x}$ exist

Prove that $\lim_{x \to \infty} \frac{\log(1+e^x)}{x} = 1$

Calculate $\lim_{x\to \infty}(\frac{\sqrt[x]{2} + \sqrt[x]{3}} {\sqrt[x]{4} + \sqrt[x]{5}})^x$

Solving $\lim\limits_{x\to0} \frac{x - \sin(x)}{x^2}$ without L'Hospital's Rule.

Proof of $\lim\limits_{x‎\to‎ 0} \frac{e - (1+x)^\frac{1}{x}}{x}=\frac{e}{2}$ [duplicate]

How to find $\lim\limits_{x\to0}\frac{e^x-1-x}{x^2}$ without using l'Hopital's rule nor any series expansion?

how can I use taylor series to approximate these two functions?

$\lim_{x\to0} \frac{x-\sin x}{x-\tan x}$ without using L'Hopital

Calculating the limit $\lim_{x \to 0} \frac{1 + \sin x - \cos x + \ln(1-x)}{x^3}$ without using l'Hospital rule or Taylor series

Evaluate $\lim_{x \to 0} \frac{\ln\left[\frac{(1-3x)(1+x)^3}{(1+3x)(1-x)^3}\right]}{x^3}$ without L'Hôpital/Taylor/differentiation/integration

How to find $\lim_{n\to \infty} \frac{\log(n)}{n}$ without L'Hospital's rule? [duplicate]

What's wrong with l'Hopital's rule?

Evaluation of $\lim\limits_{x\rightarrow0} \frac{\tan(x)-x}{x^3}$

Determine $\lim_{x \to 0}{\frac{x-\sin{x}}{x^3}}=\frac{1}{6}$, without L'Hospital or Taylor

Show $\lim_{h\to 0} \frac{(a^h-1)}{h}$ exists without l'Hôpital or even referencing $e$ or natural log

Find $\lim_\limits{x\to -\infty}{\frac{\ln\left(1+3^x\right)}{\ln\left(1+2^x\right)}}$

How can I approximate these two functions?

Are all limits solvable without L'Hôpital Rule or Series Expansion

How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?