Question

Find the limit of the function algebraically. (2 points)

limit as x approaches nine of quantity x squared minus eighty one divided by quantity x minus nine.

Answer 1

`\lim\limits_(x\to9)(x^2-81)/(x-9)=\lim\limits_(x\to9)(x^2-9^2)/(x-9)=\lim\limits_(x\to9)((x+9)(x-9))/(x-9)=\lim\limits_(x\to9)(x+9)=\\\\\\=9+9=\boxed{18}`

Answer 2

Answer: The required value of the limit is 18.

Step-by-step explanation: We are given to find the limit of the following function algebraically :

limit as x approaches nine of quantity x squared minus eighty one divided by quantity x minus nine.

We will be using the following factorization formula :

`a^2-b^2=(a+b)(a-b).`

The limit can be calculated as follows :

`\ell\\\\\\=\lim_(x\rightarrow 81)(x^2-81)/(x-9)\\\\\\=\lim_(x\rightarrow 9)(x^2-9^2)/(x-9)\\\\\\=\lim_(x\rightarrow 9)((x+9)(x-9))/((x-9))\\\\=\lim_(x\rightarrow 9)(x+9)~~~~~~~~~~~~~~~~[\textup{since }x\rightarrow 9,~so~x\\eq 9]\\\\=9+9\\\\=18.`

Thus, the required value of the limit is 18.