How do you find the limit of #(1 – 1/x)^x# as x approaches infinity?
How do you find the limit of #(1 – 1/x)^x# as x approaches infinity? Risposta: The limit is #1/e# Spiegazione: #lim_(xrarroo)(1-1/x)^x# has the form #1^oo# che è una forma indeterminata. We will use logarithms and the exponential function. Adesso, #(1-1/x)^x = e^(ln(1-1/x)^x)# So we will investigate the limit of the exponent. #lim_(xrarroo)(ln(1-1/x)^x)# It will be … Leggi tutto