(3) $lim_{x \to - \infty} \frac{2^{x + 1}}{3^{x}} =$
(a) $- \infty$
(b) $\infty$
(c) 1
(d) 0
(e) -1

Answer

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Answer

Find the limit as x approaches negative infinity: $lim_{x \to - \infty} \frac{2^{x} \cdot 2}{3^{x}} = \infty$

Steps

Step 1 ：Rewrite the function as a single exponential function: $\frac{2^{x + 1}}{3^{x}} = \frac{2^{x} \cdot 2}{3^{x}}$

Step 2 ：Find the limit as x approaches negative infinity: $lim_{x \to - \infty} \frac{2^{x} \cdot 2}{3^{x}} = \infty$