Herrera Adkins
01/10/2024 · Elementary School
2.2. Use the formal definition of a limit to show that \( \lim _{x \rightarrow 3} 2 x^{2}=18 \) QUESTION 3 [16 MARKS]
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To prove \( \lim_{x \rightarrow 3} 2x^2 = 18 \), we need to show that for any \( \epsilon > 0 \), there exists a \( \delta > 0 \) such that \( |2x^2 - 18| < \epsilon \) whenever \( 0 < |x - 3| < \delta \). We can choose \( \delta = \min\left(1, \frac{\epsilon}{14}\right) \) to satisfy this condition.
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