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Questions › DSE › DSE 2020 › Q32
4 marks, −1Mathematics › Real analysis › Supremum, infimum and epsilon argumentsModerateabout 3 min

DSE 2020 Question 32: Real analysis

Suppose u:R→R+u:\mathbb{R}\to\mathbb{R}_+u:R→R+​ is strictly increasing with supremum (least upper bound) α∈R\alpha\in\mathbb{R}α∈R. Then the function x↦u(x)α−u(x)x\mapsto \dfrac{u(x)}{\alpha-u(x)}x↦α−u(x)u(x)​ is

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Suppose u:ℝ→ℝ₊ is strictly increasing with supremum (least upper bound) α∈ℝ. Then the function x↦ u(x)/(α-u(x)) is (A) not well defined for some x∈ℝ (B) bounded above (C) unbounded above (D) not strictly increasing

Also written as: Suppose u:R->R_+ is strictly increasing with supremum (least upper bound) alpha in R. Then the function x|-> u(x)/(alpha-u(x)) is

Real analysis has come up 38 times in 5 exams since 2005.

What this question tests

This question is on Supremum, infimum and epsilon arguments, part of Real analysis in Mathematics.

Greatest lower and least upper bounds, and proofs that work with arbitrarily small tolerances.

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Question from the DSE 2020 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.