1969 AHSME Problems/Problem 35
Problem
Let be the coordinate of the left end point of the intersection of the graphs of and , where . Let . Then, as is made arbitrarily close to zero, the value of is:
Solutions
Solution 1
Since is the coordinate of the left end point of the intersection of the graphs of and , we can substitute for and find the lowest solution . That means and . That means Since plugging in for results in , there is a removable discontinuity. Multiply the fraction by to get Now there wouldn't be a problem plugging in for . Doing so results in , so the answer is .
Solution 2
From Solution 1, and , so Since is arbitrarily close to , we wish to find Using L'Hopital's Rule, the limit is equivalent to Calculating the limit shows that is .
See Also
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