limit as x approaches 7 of (x+6)/(x+1) — step-by-step solution | Explain MAths

limit as x approaches 7 of (x+6)/(x+1)

Let's evaluate the limit of

\frac{x + 6}{x + 1}

when

x \to 7

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

The limit of

x + 6

is

7 + 6

when

x \to 7

⇥Let's calculate:

7 + 6

⇥ⓘ Start from

7

and move forward

6

on the number line:

7 + 6

=

13

⇥

13

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

The limit of

x + 1

is

7 + 1

when

x \to 7

⇥Let's evaluate:

7 + 1

⇥ⓘ Start from

7

and move forward

1

on the number line:

7 + 1

=

8

⇥

8

So the limit of

\frac{x + 6}{x + 1}

is

\frac{13}{8}

when

x \to 7

▶Limit:

\frac{13}{8}

The numeric value of:

\frac{13}{8}

is:

▷

1.625