How to Work with the Intermediate Value Theorem?
A step-by-step guide to working with the intermediate value theorem Working with the Intermediate Value Theorem – Example 1: First, find the values of the given function at the \(x=0\) and \(x=2\). Substitute \(x=0\): \(f(x)=x^5-2x^3-2=0\) → \(f(0)=(0)^5-2(0)^3-2\) \(f(0)=-2\) Substitute \(x=2\): \(f(x)=x^5-2x^3-2=0\) → \(f(2)=(2)^5-2(2)^3-2\) \(f(2)=32-16-2\) \(f(2)=14\) Therefore, we conclude that at \(x = 0\), the curve […]
Connecting Limits at Infinity and Horizontal Asymptotes
A horizontal asymptote is a horizontal line that tells you how a function behaves at the edges of a graph. The following step-by-step guide talk about limits at infinity and horizontal asymptotes.
