Exam (elaborations)
MAT137 Exams A+ Graded
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Example 4.1.1 a) Solve the inequality |x − 1| − |x − 3| ≥ 5.
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1 Absolute Values & Inequations 绝对值 & 不等式解不等式主要都是我们初高中之前所学的内容。在 MAT137 这门课程中，解不等式，尤其是解带
有绝对值的不等式将会是本章节极限证明的一个重要基础工具，所以我们首先来复习一些最为常
用的解绝对值不等式的技巧，同时，我们需要掌握并记忆一些非常重要的不等式的性质。
1.1 使用分类讨论方法解不等式
Example 4.1.1
a) Solve the inequality |x − 1| − |x − 3| ≥ 5.
03
46
_
■
1+ex
b) Solve the inequality 1−ex
< 2 for x ∈ R.
1
24060194701
, 1.2 |x − a| < r 相关变形不等式的代数求解和几何意义
• |x − a| < r
• |x − a| ≤ r
• 0 < |x − a| < r
• r1 < |x − a| < r2
代数求解 & 几何分析
03
46
Example 4.2.1
_
Construct an inequality with solutions a, b ∈ R, 0 < a < b.
a) x ∈ (a − b, a) ∪ (a, a + b)
■
b) x ∈ (a − b, a) ∩ (a, a + b)
{ a+b }
c) x ∈ [a, b] \ 2
2
24060194701
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