limit as x approaches infinity of L(x)(x)^3E(x)E(x)E(x)E(x)E(x)E(x)E(x)E(x)E(x)E(x)E(x)(x)^xW(x)

解

x \to \infty lim (L (x) (x)^{3} E (x) E (x) E (x) E (x) E (x) E (x) E (x) E (x) E (x) E (x) E (x) (x)^{x} W (x))

\infty

解答ステップ

x \to \infty lim (L (x) x^{3} E (x) E (x) E (x) E (x) E (x) E (x) E (x) E (x) E (x) E (x) E (x) x^{x} W (x))

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

不定形式の場合を除く

= x \to \infty lim (L (x)) \cdot x \to \infty lim (x^{3}) \cdot x \to \infty lim (E (x)) \cdot x \to \infty lim (E (x)) \cdot x \to \infty lim (E (x)) \cdot x \to \infty lim (E (x)) \cdot x \to \infty lim (E (x)) \cdot x \to \infty lim (E (x)) \cdot x \to \infty lim (E (x)) \cdot x \to \infty lim (E (x)) \cdot x \to \infty lim (E (x)) \cdot x \to \infty lim (E (x)) \cdot x \to \infty lim (E (x)) \cdot x \to \infty lim (x^{x}) \cdot x \to \infty lim (W (x))

x \to \infty lim (L (x)) = L (\infty)

x \to \infty lim (x^{3}) = \infty

x \to \infty lim (E (x)) = E (\infty)

x \to \infty lim (x^{x}) = \infty

x \to \infty lim (W (x)) = W (\infty)

= L \cdot \infty \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot \infty \cdot W \cdot \infty

簡素化

L \cdot \infty \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot E \cdot \infty \cdot \infty \cdot W \cdot \infty : \infty

= \infty