Q. 6 - Calculus

Question

In our proof that linear functions are continuous, we used the fact that given any $\in >0$ , the choice of δ = $\frac{\in }{\left|m\right|}$ will work in the formal definition of limit. Use a graph to explain why this makes intuitive sense. (This exercise depends on Section 1.3.)

Step-by-Step Solution

Answer

Graph

Step 1. Given information

Linear functions are continuous.

Step 2. Graph

For example, take a constant function $\underset{x\to 4}{\lim }(2x+1)=9$, take δ = $0.5$, which is δ = $\frac{\in }{2}$, then it looks right for $\in =1$.

The graph is shown below :-