Question

Evaluate the limit lim x→∞ 6e4x^−e−2x
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8e^4x−e^2x3e^−x


a.3
--
4

b.1
--
4

c.1
--
2

d.3
--
5

Answer 1

Answer to Question #87288 – Math – Calculus

Question

1. Evaluate the limit

$$lim_{x \to \infty} \frac{6e^{4x} - e^{-2x}}{8e^{4x} - e^{2x} + 3e^{-x}}$$

2. Evaluate the limit

$$\lim_{x \to \infty} \frac{6e^{4x} - e^{-2x}}{8e^{4x} - e^{2x} + 3e^{-x}} = \lim_{x \to \infty} \frac{e^{4x}(6 - e^{-6x})}{e^{4x}(8 - e^{-2x} + 3e^{-5x})} = \lim_{x \to \infty} \frac{(6 - e^{-6x})}{(8 - e^{-2x} + 3e^{-5x})} = \frac{6}{8} = \frac{3}{4}$$

Note: $\lim_{x \to \infty} e^{-ax} = 0, a > 0$.

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