Limit help

[aleksqndar]

What do?

 

[tkhunny]

Introduce a logarithm.

 

[pka]

View attachment 12721
What do?

\(\displaystyle \begin{align*}\mathop {\lim }\limits_{x \to \infty } {\left( {\frac{{ax + b}}{{ax - b}}} \right)^{ax + c}}&=\mathop {\lim }\limits_{x \to \infty } {\left( {1+\frac{{2b}}{{ax - b}}} \right)^{ax + c}} \\&=\mathop {\lim }\limits_{x \to \infty } {\left( {1+\frac{{2b}}{{ax - b}}} \right)^{ax }\cdot\mathop {\lim }\limits_{x \to \infty } {\left( {1+\frac{{2b}}{{ax - b}}} \right)^{ c}}}\\&=~? \end{align*}\)


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