Problem

1) $\lim _{x \rightarrow \infty} \frac{5 x^{2}+3 x+1}{2 x^{2}+4 x-7}$

Answer

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Answer

As \(x\) approaches infinity, the terms with \(x\) in the denominator approach 0: \(\boxed{\frac{5}{2}}\)

Steps

Step 1 :Divide both the numerator and the denominator by \(x^2\): \(\frac{5 + \frac{3}{x} + \frac{1}{x^2}}{2 + \frac{4}{x} - \frac{7}{x^2}}\)

Step 2 :As \(x\) approaches infinity, the terms with \(x\) in the denominator approach 0: \(\boxed{\frac{5}{2}}\)

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