limit x->infinity (x^2+1)/x^2 — step-by-step solution | Explain MAths

limit x->infinity (x^2+1)/x^2

Compute the limit of

\frac{x^{2} + 1}{x^{2}}

as

x \to +∞

The limit of

x^{2}

is

+∞

when

x \to +∞

The limit of

x^{2} + 1

is

+∞

when

x \to +∞

For

\frac{x^{2} + 1}{x^{2}}

, the limit takes the indeterminate form

\frac{+∞}{+∞}

when

x

→

+∞

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

\frac{x^{2} + 1}{x^{2}}

into

1 + \frac{1}{x^{2}}

The limit of

\frac{1}{x^{2}}

is

0

⁺ when

x \to +∞

The limit of

1 + \frac{1}{x^{2}}

is

1

when

x \to +∞

So the limit of

\frac{x^{2} + 1}{x^{2}}

is

1

when

x \to +∞

▷Result: $1$