Ali is trying to find the limit of a function which is expressed as L = lim x→0+ (1 + x)1/x . From his understanding, the quantity (1 + x), must be greater than 1 for x > 0. Furthermore, the power1 / x is going to infinity as ? approaches 0 from the right. So L is the result of taking a number greater than 1 to higher power, therefore L = ∞. On the other hand, he sees that (1 + x) is approaching 1 as x approaches 0, and 1 taken to any power whatever is 1. Ali concluded, L = 1. Help Ali by pointing out to him the error of his ways.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Ali is trying to find the limit of a function which is expressed as L = lim x→0+ (1 + x)1/x . From his understanding, the quantity (1 + x), must be greater than 1 for x > 0. Furthermore, the power1 / x is going to infinity as ? approaches 0 from the right. So L is the result of taking a number greater than 1 to higher power, therefore L = ∞. On the other hand, he sees that (1 + x) is approaching 1 as x approaches 0, and 1 taken to any power whatever is 1. Ali concluded, L = 1. Help Ali by pointing out to him the error of his ways.

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