Question

Lim_(x-1)(2x^(2)-9x+9)/(x-3)=

Answer 1

`\lim_(x\to 1)(2x^2-9x+9)/(x-3)=-1`.

Explanation:

Consider the given limit problem is

`\lim_(x\to 1)(2x^2-9x+9)/(x-3)=?`

We need to find the value of given limit problem.

Taking limit, we get

`\lim_(x\to 1)(2x^2-9x+9)/(x-3)=(2(1)^2-9(1)+9)/((1)-3)`

`\lim_(x\to 1)(2x^2-9x+9)/(x-3)=(2-9+9)/(-2)`

`\lim_(x\to 1)(2x^2-9x+9)/(x-3)=(2)/(-2)`

`\lim_(x\to 1)(2x^2-9x+9)/(x-3)=-1`

Therefore,
`\lim_(x\to 1)(2x^2-9x+9)/(x-3)=-1`.