The Formal Version Examples
Example 1
Let f(x) = 2x, c = 4, and ε = 0.5. Find an appropriate δ > 0, so that if x is within δ of 4, f(x) will be within ε of f(c). |
Example 2
Let f(x) = x^{2}, c = 2, and ε = 0.1. What is an appropriate value of δ > 0, that will guarantee that if |x – c| < δ, |f(x) – f(c)| < ε? |
Example 3
Let f(x) = 4x + 1. Find a value of δ such that if |x – 5| < δ, then |f(x) – f(5)| < 0.1. |
Example 4
Let f(x) = sin(x) Find a value of δ such that if , then . |
Example 5
Let . Find a value of δ such that if |x – 2| < δ, then |f(x) – 0.5| < 0.005. |
Example 6
Let . What is a value of δ that will guarantee that if |x – 7| < δ, then ? |