Difference between revisions of "1950 AHSME Problems/Problem 40"
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Note: Alternatively, we can ignore the domain restriction and just plug in <math>x = 1</math> into the reduced expression. | Note: Alternatively, we can ignore the domain restriction and just plug in <math>x = 1</math> into the reduced expression. | ||
| − | ~cxsmi | + | ~ [https://artofproblemsolving.com/wiki/index.php/User:Cxsmi cxsmi] |
{{AHSME 50p box|year=1950|num-b=39|num-a=41}} | {{AHSME 50p box|year=1950|num-b=39|num-a=41}} | ||
Latest revision as of 12:43, 4 April 2024
Problem
The limit of 
as 
approaches 
as a limit is:
Solution
Both 
and 
approach 0 as approaches , using the L'Hôpital's rule, we have 
.
Thus, the answer is 
.
~ MATH__is__FUN
Solution 2
The numerator of can be factored as 
. The terms in the numerator and denominator cancel, so the expression is equal to 
so long as does not equal . Looking at the function's behavior near 1, we see that as approaches one, the expression approaches .
Note: Alternatively, we can ignore the domain restriction and just plug in 
into the reduced expression.
~ cxsmi
| 1950 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 39 |
Followed by Problem 41 | |
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| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
