[latex] \lim_{x \to \ o} (1+3x)^{ \frac{-1}{2x}} [/latex]

Question

[latex] \lim_{x \to \ o} (1+3x)^{ \frac{-1}{2x}} [/latex]

Алгебра

Гость

Ответ(ы) на вопрос:

Accepted Answer

[latex]\lim_{x \to \ 0} (1+3x)^{ \frac{-1}{2x}}=\lim_{x \to \ 0} (1+3x)^{ \frac{-1}{2x}*3x*\frac{1}{3x}}=e^{\lim_{x \to \ 0}\frac{-1*3x}{2x}}=\\\\=e^\frac{-3}2}=\frac{1}{\sqrt{e^3}}[/latex]

﻿[latex] \lim_{x \to \ o} (1+3x)^{ \frac{-1}{2x}} [/latex]

[latex] \lim_{x \to \ o} (1+3x)^{ \frac{-1}{2x}} [/latex]