객관식
Evaluate the following limit: .
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23. Intro to Derivatives & Area Under the Curve
Limits at Infinity
객관식
Evaluate the following limit: .
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검증된 단계별 안내1
Identify the limit expression: \( \lim_{x \to \infty} \frac{x+7}{8x-100} \).
To evaluate the limit as \( x \to \infty \), divide every term in the numerator and the denominator by \( x \), the highest power of \( x \) in the denominator.
Rewrite the expression: \( \frac{x+7}{8x-100} = \frac{\frac{x}{x} + \frac{7}{x}}{\frac{8x}{x} - \frac{100}{x}} = \frac{1 + \frac{7}{x}}{8 - \frac{100}{x}} \).
As \( x \to \infty \), the terms \( \frac{7}{x} \) and \( \frac{100}{x} \) approach 0.
Thus, the limit simplifies to \( \frac{1 + 0}{8 - 0} = \frac{1}{8} \).
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