limit of x/(x+1) when x tends to infinity — step-by-step solution | Explain MAths

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

Compute the limit of

\frac{x}{x + 1}

as

x \to +∞

The limit of

x + 1

is

+∞

when

x \to +∞

For

\frac{x}{x + 1}

, the limit takes the indeterminate form

\frac{+∞}{+∞}

when

x

→

+∞

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

\frac{x}{x + 1}

into

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

The limit of

\frac{1}{x}

is

0

⁺ when

x \to +∞

The limit of

1 + \frac{1}{x}

is

1

when

x \to +∞

The limit of

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

is

1

when

x \to +∞

So the limit of

\frac{x}{x + 1}

is

1

when

x \to +∞

▷Result: $1$