Someone can help with this question ? (the value of K)
E EstudanteQuimica New member Joined Oct 9, 2020 Messages 2 Oct 9, 2020 #1 Someone can help with this question ? (the value of K)
Dr.Peterson Elite Member Joined Nov 12, 2017 Messages 16,087 Oct 9, 2020 #2 I would apply l'Hopital to the log of the limit.
skeeter Elite Member Joined Dec 15, 2005 Messages 3,215 Oct 9, 2020 #4 [math]\left(1+\dfrac{k+20}{x} + \dfrac{20k}{x^2}\right)^x[/math] [MATH]\left(\dfrac{(x+k)(x+20)}{x^2}\right)^x[/MATH] [MATH]\left(\dfrac{x+k}{x} \cdot \dfrac{x+20}{x}\right)^x[/MATH] [MATH]\left(\dfrac{x+k}{x}\right)^x \cdot \left(\dfrac{x+20}{x}\right)^x[/MATH] [MATH]\lim_{x \to \infty}\left(\dfrac{x+k}{x}\right)^x \cdot \lim_{x \to \infty} \left(\dfrac{x+20}{x}\right)^x[/MATH] [MATH]e^k \cdot e^{20} = e^{60}[/MATH]
[math]\left(1+\dfrac{k+20}{x} + \dfrac{20k}{x^2}\right)^x[/math] [MATH]\left(\dfrac{(x+k)(x+20)}{x^2}\right)^x[/MATH] [MATH]\left(\dfrac{x+k}{x} \cdot \dfrac{x+20}{x}\right)^x[/MATH] [MATH]\left(\dfrac{x+k}{x}\right)^x \cdot \left(\dfrac{x+20}{x}\right)^x[/MATH] [MATH]\lim_{x \to \infty}\left(\dfrac{x+k}{x}\right)^x \cdot \lim_{x \to \infty} \left(\dfrac{x+20}{x}\right)^x[/MATH] [MATH]e^k \cdot e^{20} = e^{60}[/MATH]