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Chapter 1: Q. 58 (page 149)

Calculate each limit in Exercises 35鈥�80.
$\underset{x 鈫� 鈭�}{l i m} \frac{2^{x} - 4^{- x}}{3^{x}}$

Short Answer

Expert verified

The limit is 0

Step by step solution

01

Step 1. Given information

The given expression is $\underset{x 鈫� 鈭�}{l i m} \frac{2^{x} - 4^{- x}}{3^{x}}$

02

Step 2. Calculation

The limit is calculated as below,

$\underset{x 鈫� 鈭�}{l i m} \frac{2^{x} - 4^{- x}}{3^{x}} = \underset{x 鈫� 鈭�}{l i m} (\frac{2^{x} - \frac{1}{4^{x}}}{3^{x}} 脳 \frac{\frac{1}{3^{x}}}{\frac{1}{3^{x}}}) = \underset{x 鈫� 鈭�}{l i m} (\frac{{(\frac{2}{3})}^{x} - {(\frac{1}{12})}^{x}}{1}) = (\frac{{(\frac{2}{3})}^{鈭�} - {(\frac{1}{12})}^{鈭�}}{1}) = \frac{0 - 0}{1} = 0$

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Most popular questions from this chapter

Write delta-epsilon proofs for each of the limit statements in Exercises $47 鈥� 60 .$

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$\lim_{x 鈫� 1} \frac{x^{2} - 1}{x - 1} = 2$

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