Practice Edge Cases in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Special or extreme input values — such as zero, infinity, empty sets, or boundary conditions — where formulas or reasoning may behave differently.
What happens at the extremes? When x = 0? When x \to \infty? When inputs are unusual?
Example 1
easyFor the function f(x) = \dfrac{x^2-4}{x-2}, check the edge case x = 2 and describe what happens.
Example 2
mediumCheck all edge cases for the statement: 'For natural numbers n, \dfrac{n!}{(n-1)!} = n.' Test n = 0 and n = 1.
Example 3
easyFor f(x) = \sqrt{x}, identify the edge case and state the domain.
Example 4
mediumTest the edge cases n=0 and n=1 for the formula \sum_{k=1}^{n} k = \frac{n(n+1)}{2}.