limit as x--> infinity of 1/(1+e^x)^2 Solution Take the limit: lim_(x->infinity)

Question

limit as x--> infinity of 1/(1+e^x)^2

Explanation / Answer

Take the limit: lim_(x->infinity) 1/(1+e^x)^2 The limit of a quotient is the quotient of the limits: The limit of a constant is the constant: = 1/(lim_(x->infinity) (1+e^x)^2) Using the power law, write lim_(x->infinity) (1+e^x)^2 as (lim_(x->infinity) (1+e^x))^2: = 1/(lim_(x->infinity) (1+e^x))^2 The limit of a constant is the constant: The limit of a sum is the sum of the limits: = 1/(1+lim_(x->infinity) e^x)^2 The limit of e^x as x approaches infinity is infinity: Answer: | | = 0

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