Difference between revisions of "1950 AHSME Problems/Problem 40"
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{{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 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
