Задача 58897 ...

6060726f1ba1332da0acdc7b

31.03.2021 13:39:47

11.2.41. lim (1 + 3/x)^((x^2)/(x+y))
x→+∞
y→5

5f3ea7e3faf909182968ddd9

31.03.2021 16:11:28

★

[m]lim_{x → ∞ }(1+\frac{3}{x})^{\frac{x}{3}}=e[/m]


[m]lim_{x → ∞,y → 5 }(1+\frac{3}{x})^{\frac{x^2}{x+y}}=[/m]

[m]=(lim_{x → ∞ }(1+\frac{3}{x})^{\frac{x}{3}})^{lim_{x → ∞,y → 5}\frac{3}{x}\cdot \frac{x^2}{x+y} }=[/m]

[m]=e^{lim_{x → ∞,y → 5 }\frac{3x}{x+y}}=e^{3}[/m]