Difference between revisions of "1950 AHSME Problems/Problem 37"
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\textbf{(B)}\ \text{If }x=a,y=1 \qquad\ | \textbf{(B)}\ \text{If }x=a,y=1 \qquad\ | ||
\textbf{(C)}\ \text{If }x=-1,y\text{ is imaginary (complex)} \qquad\ | \textbf{(C)}\ \text{If }x=-1,y\text{ is imaginary (complex)} \qquad\ | ||
− | \textbf{(D)}\ \text{If }0<x< | + | \textbf{(D)}\ \text{If }0<x<1,y\text{ is always less than 0 and decreases without limit as }x\text{ approaches zero} \qquad\ |
\textbf{(E)}\ \text{Only some of the above statements are correct}</math> | \textbf{(E)}\ \text{Only some of the above statements are correct}</math> | ||
Revision as of 16:08, 15 March 2017
Problem
If , , which of the following statements is incorrect?
Solution
Let us first check
. Rewriting into exponential form gives . This is certainly correct.
. Rewriting gives . This is also certainly correct.
. Rewriting gives . Because , therefore positive, there is no real solution to , but there is imaginary.
. Rewriting: such that . Well, a power of can be less than only if . And we observe, has no lower asymptote, because it is perfectly possible to have be ; in fact, the lower gets, approaches . This is also correct.
. This is the last option, so it follows that our answer is
See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 36 |
Followed by Problem 38 | |
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All AHSME Problems and Solutions |
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