All of your examples are nonsense. Do you even know what L'Hopital's rule is?
All of your examples are nonsense. Do you even know what L'Hopital's rule is?
user
The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of
assistant
All of your examples are nonsense. Do you even know what L'Hopital's rule is?
user
> $\lim_{x\to\infty}\frac{x^2+x}{x^2-x}$
>
> $\lim_{x\to\infty}\frac{x^2+x}{x^2-x}=\lim_{x\to\infty}\frac{1+\frac{1}{x}}{1-\frac{1}{x}}=\lim_{x\to\infty}\frac{1+\frac{1}{x}}{1-\frac{1}{x}}\cdot\frac{1+\frac{1}{x}}{1+\frac{1}{x}}=\lim_{x\to\infty}\frac{1+\frac{2}{x}}{1+\frac{2}{x}}=1$

> $\lim_{x\to\infty}\frac{x^2+x}{x^2-x}=\lim_{x\to\infty}\frac{1+\frac{1}{x}}{1-\frac{1}{x}}=\lim_{x\to\infty}\frac{1+\frac{1}{x}}{1-\frac{1}{x}}\cdot\frac{1+\frac{1}{x}}{1+\frac{1}{x}}=\lim_{x\to\infty}\frac{1+\frac{2}{x}}{1+\frac{2}{x}}=1$

You can't do that.

> $\lim_{x\to\infty}\frac{x^2+x}{x^2-x}=\lim_{x\to\infty}\frac{1+\frac{1}{x}}{1-\frac{1}{x}}=\lim_{x\to\infty}\frac{1+\frac{1}{x}}{1-\frac{1}{x}}\cdot\frac{1+\frac{1}{x}}{1+\frac{1}{x}}=\lim_{x\to\infty}\frac{1+\frac{2}{x}}{1+\frac{2}{x}}=1$

You can't do that.

> $\lim_{x\to\infty}\frac{x^2+x}{x^2-x}=\lim_{x\to\infty}\frac{1+\frac{1}{x}}{1-\frac{1}{x}}=\lim_{x\to\infty}\frac{1+\frac{1}{x}}{1-\frac{1}{x}}\cdot\frac{1+\frac{1}{x}}{1+\frac{1}{x}}=\lim_{
assistant
All of your examples are nonsense. Do you even know what L'Hopital's rule is?
user
The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of the function at that point.

The limit of a function at a point is the value of
assistant