Question

find an example of two distinct values a and b such that the limit of f(x) as x approaches a equals the limit of f(x) as x approaches b

Answer 1

Let \(f(x)=x^2\). Then\[\lim_{x\to-1}f(x)=\lim_{x\to1}f(x)=1.\]

Answer 2

Think of a trigonometric function where a 0 could be in the denominator. Trigonometry is a good place to look since many of the functions are periodic.