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Mathematics LibreTexts

2.4E: Infinite Limits EXERCISES

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    10236

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    2.4: Infinite Limit Exercises 

    In the following exercises, find the limit.

    100) \(\displaystyle \lim_{x→1}\frac{x^3−1}{x^2−1}\)

    101) \(\lim_{x→1/2}\frac{2x^2+3x−2}{2x−1}\)

    Answer:
     \(lim_{x→1/2}\frac{2x^2+3x−2}{2x−1}=\frac{\frac{1}{2}+\frac{3}{2}−2}{1−1}=\frac{0}{0}; then, lim_{x→ 1/2}\frac{2x^2+3x−2}{2x−1}=lim_{x→1/2}frac{(2x−1)(x+2)}{2x−1}=\frac{5}{2}\)

    102) \(lim_{x→−3}\frac{\sqrt{x+4}−1}{x+3}\)

    103) \(lim_{x→−2^−}\frac{2x^2+7x−4}{x^2+x−2}\)

    Answer:
    −∞

    104) \(lim_{x→−2^+}\frac{2x^2+7x−4}{x^2+x−2}\)

    105) \(lim_{x→1^−}\frac{2x^2+7x−4}{x^2+x−2}\)

    Answer:
    −∞

    106) \(lim_{x→1^+}\frac{2x^2+7x−4}{x^2+x−2}\)