Short Answer

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| < $ε$ .
$\lim_{x \to 0} (5 x^{2} - 1) = - 1$

$δ = \sqrt{\frac{ε}{5}}$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step1. Given information.

We have been given a limit statement as $\lim_{x \to 0} (5 x^{2} - 1) = - 1$ .

We have to find $δ in terms of ε$ .

Step 2. Use algebra.

From the given limit statement, we can identify

$f (x) = 5 x^{2} - 1 c = 0 L = - 1 For ε > 0 |(5 x^{2} - 1) - (- 1)| < ε |5 x^{2} - 1 + 1| < ε |5 x^{2}| < ε 5 |x^{2}| < ε |x^{2}| < \frac{ε}{5} | x | < \sqrt{\frac{ε}{5}} F o r 0 < | x - 0 | < δ, w e g e t | x | < \sqrt{\frac{ε}{5}} Therefore, δ = \sqrt{\frac{ε}{5}}$

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Calculus

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Short Answer

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| < $ε$ .
$\lim_{x \to 0} (5 x^{2} - 1) = - 1$

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→0(5x2-1)=-1

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| < $ε$ .
$\lim_{x \to 0} (5 x^{2} - 1) = - 1$