Evaluate the limit Lim (1 + (2/x))²x→∞
To evaluate the limit, we can first apply some algebraic manipulations to simplify the expression
To evaluate the limit, we can first apply some algebraic manipulations to simplify the expression.
Starting with the expression (1 + (2/x))^2 as x approaches infinity, we can rewrite it as follows:
(1 + (2/x))^2 = [(1 + (2/x))/1]^2
Next, we can simplify the expression within the square brackets:
[(1 + (2/x))/1]^2 = [(x + 2)/x]^2
Now, let’s evaluate the limit as x approaches infinity:
Lim x→∞ [(x + 2)/x]^2
To evaluate this limit, we can consider the highest degree terms in the numerator and denominator, which in this case are x. By dividing both the numerator and denominator by x^2, we get:
Lim x→∞ [(x + 2)/x]^2 = Lim x→∞ [(1 + (2/x))/1]^2
= Lim x→∞ [(1/x + 2/x^2)/1]^2
= Lim x→∞ [(0 + 0)/1]^2
= (0/1)^2
= 0
Therefore, the limit of (1 + (2/x))^2 as x approaches infinity is equal to 0.
More Answers:
Evaluating the Limit of (x+2)/((√(x^2-4))) as x approaches 2Evaluating the Limit of (tan(x)/sec(x)) as x Approaches 0 using Trigonometric Simplifications
Evaluate the Limit of ln(2x)/x Using L’Hôpital’s Rule as x Approaches Infinity