Question

Find the limit of the function by using direct substitution.

limit as x approaches zero of quantity x squared minus one.

Answer 1

-1

Explanation:

For direct substitution, all you have to do is fill in the limit for x and solve... so the limit would be 0 in this case.

x^2-1

0^2-1

-1

Answer 2

`lim_(x \to \: 0)( {x}^(2) - 1) = - 1`

EXPLANATION

The given limit is

`lim_(x \to \: 0)( {x}^(2) - 1)`

To evaluate this limit by direct substitution,

We put x=0 in the function.

This implies that that ,

`lim_(x \to \: 0)( {x}^(2) - 1) = {0}^(2) - 1`

This simplifies to,

`lim_(x \to \: 0)( {x}^(2) - 1) = 0 - 1`

`lim_(x \to \: 0)( {x}^(2) - 1) = - 1`

This means that as x-values approach zero, the function approaches -1.