Question-107124

Question Number 107124 by Khalmohmmad last updated on 08/Aug/20

Answered by mathmax by abdo last updated on 08/Aug/20

let f (x) = \frac{3^{π x} - 1}{π x} we have 3^{π x} = e^{π xln (3)} = 1 + π xln (3) + o (x^{2}) \Rightarrow

\frac{e^{π xln 3} - 1}{π x} = \ln (3) + o (x) \Rightarrow \lim_{x \to 0} f (x) = \ln (3)

Answered by JDamian last updated on 08/Aug/20

3^{π x} = 1 + \frac{π \ln 3}{1!} x + \frac{{(π \ln 3)}^{2}}{2!} x^{2} + \cdot \cdot \cdot

\lim_{x \to 0} (\frac{3^{π x} - 1}{π x}) = \lim_{x \to 0} (\ln 3 + \frac{{(π \ln 3)}^{2}}{2! π} x + \cdot \cdot \cdot) =

= \ln 3

Facebook Tweet Pin