Chapter 1: Q. 37 (page 107)

For each limit statement , use algebra to find δ > 0 in terms of $ε$ > 0 so that if 0 < |x − c| < δ, then | f(x) − L| < $ε$ .
$\lim_{x \to 2} \frac{1}{x} = \frac{1}{2}; you may assume δ \leq 1$

Short Answer

Expert verified

$δ = m i n (1, 2 ε)$

Step by step solution

Step1. Given information.

We have been given a limit statement as $\lim_{x \to 2} \frac{1}{x} = \frac{1}{2}; you may assume δ \leq 1$ .

We have to find $δ in terms of ε$ .

Step 2. Use algebra

From the given limit statement, we can identify

$f (x) = \frac{1}{x} c = 2 L = \frac{1}{2} For ε > 0 |\frac{1}{x} - \frac{1}{2}| < ε |\frac{2 - x}{2 x}| < ε \frac{1}{2} | x - 2 | < ε | x - 2 | < 2 ε For 0 < | x - c | < δ, we get | x - 2 | < 2 ε Therefore, δ = m i n (1, 2 ε)$

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For each limit statement , use algebra to find δ > 0 in terms of $ε$ > 0 so that if 0 < |x − c| < δ, then | f(x) − L| < $ε$ .
$\lim_{x \to 2} \frac{1}{x} = \frac{1}{2}; you may assume δ \leq 1$

Short Answer

Step by step solution

Step1. Given information.

Step 2. Use algebra

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For each limit statement , use algebra to find δ > 0 in terms of ε> 0 so that if 0 < |x − c| < δ, then | f(x) − L| < ε.limx→21x=12;youmayassumeδ≤1

Short Answer

Step by step solution

Step1. Given information.

Step 2. Use algebra

One App. One Place for Learning.

Most popular questions from this chapter

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For each limit statement , use algebra to find δ > 0 in terms of $ε$ > 0 so that if 0 < |x − c| < δ, then | f(x) − L| < $ε$ .
$\lim_{x \to 2} \frac{1}{x} = \frac{1}{2}; you may assume δ \leq 1$