Chapter 1: Q. 59 (page 149)

Calculate each limit in Exercises 35–80.
$\underset{x \to - \infty}{l i m} \frac{3^{x} - 5^{x}}{4^{x}}$

Short Answer

Expert verified

The limit is infinity

Step by step solution

Step 1. Given information

The given expression is $\underset{x \to - \infty}{l i m} \frac{3^{x} - 5^{x}}{4^{x}}$

Step 2. Calculation

The limit is calculated as below,

$\underset{x \to - \infty}{l i m} \frac{3^{x} - 5^{x}}{4^{x}} = = \underset{x \to - \infty}{l i m} (\frac{3^{x} - 5^{x}}{4^{x}} \times \frac{\frac{1}{4^{x}}}{\frac{1}{4^{x}}}) = \underset{x \to - \infty}{l i m} (\frac{{(\frac{3}{4})}^{x} - {(\frac{5}{4})}^{x}}{1}) = (\frac{{(\frac{3}{4})}^{- \infty} - {(\frac{5}{4})}^{- \infty}}{1}) = \frac{\infty - \infty}{1} = \infty$

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Calculate each limit in Exercises 35–80.
$\underset{x \to - \infty}{l i m} \frac{3^{x} - 5^{x}}{4^{x}}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Calculate each limit in Exercises 35–80. limx→-∞3x-5x4x

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Calculate each limit in Exercises 35–80.
$\underset{x \to - \infty}{l i m} \frac{3^{x} - 5^{x}}{4^{x}}$