Question

Lim (1+3x)^(2/5x) ×->0

Answer 1

Используем формулу второго замечательного предела

Lim(1+x)^1/x=e
x->0

Получим:

$\lim_{n \to \0} (1+3x)^{ \frac{1}{3x}*3x* \frac{2}{5x} } = e^{ \frac{3x*2}{5x} } = e^{ \frac{3*2}{5} }= e^{ \frac{6}{5} }$

Answer 2

To find the limit of the expression as x approaches 0, we can directly substitute 0 for x and evaluate the result:

lim (1 + 3x)^(2/5x) as x -> 0

Substitute x = 0:

(1 + 30)^(2/50) = 1^0 = 1

So, the limit of the expression as x approaches 0 is 1.