limit of x/(x+1) when x tends to infinity

Let's evaluate the limit of

\frac{x}{x + 1}

when

x \to +∞

ⓘ A quantity that grows without bound plus a finite or bounded quantity still grows without bound

The limit of

x + 1

+∞

when

x \to +∞

For

\frac{x}{x + 1}

, we obtain the indeterminate form

\frac{+∞}{+∞}

x

tends to

+∞

To find the limit, we can factor out the dominant term and transform

\frac{x}{x + 1}

into

\frac{1}{1 + \frac{1}{x}}

ⓘ A number divided by a quantity that grows without bound tends to 0

The limit of

\frac{1}{x}

0

⁺ when

x \to +∞

ⓘ The limit of a sum of finite limits is the sum of the limits

The limit of

1 + \frac{1}{x}

1

when

x \to +∞

The limit of

\frac{1}{1 + \frac{1}{x}}

1

when

x \to +∞

So the limit of

\frac{x}{x + 1}

1

when

x \to +∞

▶Limit:

1