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Consider the following statement about real numbers - HSC - SSCE Mathematics Extension 2 - Question 4 - 2023 - Paper 1
Question 4
Consider the following statement about real numbers. 'Whichever positive number $r$ you pick, it is possible to find a number $x$ greater than 1 such that \( \frac{... show full transcript
Worked Solution & Example Answer:Consider the following statement about real numbers - HSC - SSCE Mathematics Extension 2 - Question 4 - 2023 - Paper 1
Step 1
C. $\exists r > 0 \forall x > 1 \; \frac{\ln x}{x^3} < r$.
Answer
The correct formulation states that there exists a positive real number such that for all greater than 1, the inequality ( \frac{\ln x}{x^3} < r ) holds true. This corresponds to the essence of the original statement, which implies that no matter what positive number is chosen, a corresponding can be found that adheres to the inequality.