Answer
$\lim _{x\rightarrow 2}f\left( x\right) =\dfrac {x-2}{x^{2}-3x+2}=1$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/bb9cf444-17c5-477a-982f-e8e9aeb9276f/result_image/1508565658.jpeg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240616%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240616T120405Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=738b20f57355acdedc209d15454c25da3ab5577e2abd65830a6e439dd3c983f7)
Work Step by Step
As we see from table and graph when x gets close to 2
$f\left( x\right) =\dfrac {x-2}{x^{2}-3x+2}\rightarrow 1$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/bb9cf444-17c5-477a-982f-e8e9aeb9276f/steps_image/small_1508565658.jpeg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240616%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240616T120405Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=faf8fd1b46036b64362d5468342775df99b5b6c64511a7ea4911e389b8d0a61d)
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