Answer:
[tex]\lim_{x\to 1}\dfrac{2x^2-9x+9}{x-3}=-1[/tex].
Step-by-step explanation:
Consider the given limit problem is
[tex]\lim_{x\to 1}\dfrac{2x^2-9x+9}{x-3}=?[/tex]
We need to find the value of given limit problem.
Taking limit, we get
[tex]\lim_{x\to 1}\dfrac{2x^2-9x+9}{x-3}=\dfrac{2(1)^2-9(1)+9}{(1)-3}[/tex]
[tex]\lim_{x\to 1}\dfrac{2x^2-9x+9}{x-3}=\dfrac{2-9+9}{-2}[/tex]
[tex]\lim_{x\to 1}\dfrac{2x^2-9x+9}{x-3}=\dfrac{2}{-2}[/tex]
[tex]\lim_{x\to 1}\dfrac{2x^2-9x+9}{x-3}=-1[/tex]
Therefore, [tex]\lim_{x\to 1}\dfrac{2x^2-9x+9}{x-3}=-1[/tex].
