Q. 5 - Calculus | StudyQuestionHub

StudyQuestionHub

Q. 5

Question

In our proof that constant functions are continuous, we used the fact that given any $\in$ > 0, a choice of any δ > 0 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

Verified

Answer

Graph

1Step 1. Given information

Constant functions are continuous.

2Step 2. Graph

For example, take a constant function $\lim_{x - > 4} (2 x + 1) = 9$ , take δ = 0.5 then it looks right for $\in = 1$ .

The figure is shown below :-

Other exercises in this chapter

If f is a continuous function, what can you say about limx→1f(x)?

Explain what it means for a function f to be continuous at a point x=c, with a sentence that includes the words “approaches” and “value.&

In our proof that linear functions are continuous, we used the fact that given any ∈>0 , the choice of δ = ∈|m| will work in the

Given the following function f , define f(1) so that f is continuous at x = 1, if possible:f(x)=x2-2x+1x2-6x+5