題目 Problem Let f(x)=cos(4x)−1−xf(x)=\cos(4x)-1-xf(x)=cos(4x)−1−x and g(x)=e2x−1g(x)=e^{2x}-1g(x)=e2x−1 for x∈(−∞,∞)x\in(-\infty,\infty)x∈(−∞,∞). Which of the following statements is true? (a) limx→0+f(x)/g(x)\lim_{x\to 0^+}f(x)/g(x)limx→0+f(x)/g(x) does not exist. (b) −∞<limx→0+f(x)/g(x)≤−2-\infty<\lim_{x\to 0^+}f(x)/g(x)\le -2−∞<limx→0+f(x)/g(x)≤−2. (c) −2<limx→0+f(x)/g(x)≤−1-2<\lim_{x\to 0^+}f(x)/g(x)\le -1−2<limx→0+f(x)/g(x)≤−1. (d) −1<limx→0+f(x)/g(x)≤0-1<\lim_{x\to 0^+}f(x)/g(x)\le 0−1<limx→0+f(x)/g(x)≤0. (e) 0<limx→0+f(x)/g(x)<∞0<\lim_{x\to 0^+}f(x)/g(x)<\infty0<limx→0+f(x)/g(x)<∞. 解答 待補。
