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 13:43, 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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