題目 Problem Let f(x)=ex+sin(2x)f(x)=e^x+\sin(2x)f(x)=ex+sin(2x) and g(x)=ex+cos(2x)g(x)=e^x+\cos(2x)g(x)=ex+cos(2x) for x∈(−∞,∞)x\in(-\infty,\infty)x∈(−∞,∞). Which of the following statements is true? (a) −∞<limx→∞g(x)/f(x)≤1-\infty<\lim_{x\to\infty} g(x)/f(x)\le 1−∞<limx→∞g(x)/f(x)≤1. (b) 1<limx→∞g(x)/f(x)≤21<\lim_{x\to\infty} g(x)/f(x)\le 21<limx→∞g(x)/f(x)≤2. (c) 2<limx→∞g(x)/f(x)≤32<\lim_{x\to\infty} g(x)/f(x)\le 32<limx→∞g(x)/f(x)≤3. (d) 3<limx→∞g(x)/f(x)<∞3<\lim_{x\to\infty} g(x)/f(x)<\infty3<limx→∞g(x)/f(x)<∞. (e) limx→∞g(x)/f(x)\lim_{x\to\infty} g(x)/f(x)limx→∞g(x)/f(x) does not exist. 解答 待補。
