Chapter 1: Q. 62 (page 149)

Calculate each limit in Exercises 35–80.
$\underset{x \to \infty}{l i m} \frac{1 - 5 e^{2 x}}{3 e^{x} + 4 e^{2 x}}$

Short Answer

Expert verified

The limit is $- \frac{5}{4}$

Step by step solution

Step 1. Given information

The given expression is $\underset{x \to \infty}{l i m} \frac{1 - 5 e^{2 x}}{3 e^{x} + 4 e^{2 x}}$

Step 2. Calculation

The limit is calculated as below,

$\underset{x \to \infty}{l i m} \frac{1 - 5 e^{2 x}}{3 e^{x} + 4 e^{2 x}} = \underset{x \to \infty}{l i m} \frac{1 - 5 e^{2 x}}{3 e^{x} + 4 e^{2 x}} \times \frac{\frac{1}{e^{2 x}}}{\frac{1}{e^{2 x}}} = \underset{x \to \infty}{l i m} \frac{e^{- 2 x} - 5}{3 e^{- x} + 4} = \frac{e^{- 2 (\infty)} - 5}{3 e^{- (\infty)} + 4} = \frac{0 - 5}{3 (0) + 4} = - \frac{5}{4}$

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Calculate each limit in Exercises 35–80.
$\underset{x \to \infty}{l i m} \frac{1 - 5 e^{2 x}}{3 e^{x} + 4 e^{2 x}}$

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→∞1-5e2x3ex+4e2x

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

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Calculate each limit in Exercises 35–80.
$\underset{x \to \infty}{l i m} \frac{1 - 5 e^{2 x}}{3 e^{x} + 4 e^{2 x}}$