問題：次の式を計算せよ

• (1) \( \displaystyle \lim_{x \to \infty} \log_{\frac{1}{3}}x \)


• (2) \( \displaystyle \lim_{x \to +0} \biggl(\dfrac{1}{5}\biggr)^{\frac{1}{x}} \)


• (3) \( \displaystyle \lim_{x \to \infty} \dfrac{2^x + 5^x}{3^x + 5^x} \)


• (4) \( \displaystyle \lim_{x \to \infty} \log_{0.5}\dfrac{8x^2 + 1}{4x^2 + 2} \)


• (5) \( \displaystyle \lim_{x \to \infty} \log_{17}\dfrac{3x^3 + 2x - 5}{3x^3 + 3x^2 + 5x} \)