Explaning the limit

[trinhducx]

I have a Limit problem as below:
Connor claims: " lim (6x² + 7x + 3)/(2x³ + x² -2x - 1) = 3 with x-> infinity because my high school calculus teacher told us the limit of ratio of polynomials is always the quotient of the coefficients of the highest power terms"
If correct, show in detail how to use algebra and the limit theorems to evaluate this limit and get the same answer
If wrong,
1, use algebra and limit theorems to correctly evaluate the limit and
2, write a paragraph that explain why Connor shouldn't expect the rule he remember from high school to work in this particular problem

I am able to correctly evaluate the limit ( lim = 0) but since my first language is not English, I don't understand what Connor claimed and how to explain it. Can anyone help? Thanks in advance

 

[Ishuda]

I have a Limit problem as below:
Connor claims: " lim (6x² + 7x + 3)/(2x³ + x² -2x - 1) = 3 with x-> infinity because my high school calculus teacher told us the limit of ratio of polynomials is always the quotient of the coefficients of the highest power terms"
If correct, show in detail how to use algebra and the limit theorems to evaluate this limit and get the same answer
If wrong,
1, use algebra and limit theorems to correctly evaluate the limit and
2, write a paragraph that explain why Connor shouldn't expect the rule he remember from high school to work in this particular problem

I am able to correctly evaluate the limit ( lim = 0) but since my first language is not English, I don't understand what Connor claimed and how to explain it. Can anyone help? Thanks in advance

"the quotient of the coefficients of the highest power terms" would, in this case be 6 (the coefficient of the highest term in the numerator) divided by 2 (the coefficient of the highest term in the denominator). Obviously what was remembered is incorrect. That probably is because the complete explanation by the high school calculus teacher was not remembered correctly.