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

Answer

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Answer

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

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: $\lim_{x \to -\infty} \frac{2^x \cdot 2}{3^x} = \boxed{\infty}$