Write a delta-epsilon proof that shows that function $f(x) = 3x - 5$ is continuous at $x = 2$.
Added by Alyssa S.
Close
Step 1
A function f(x) is continuous at x = a if for any ε > 0, there exists a δ > 0 such that if |x - a| < δ, then |f(x) - f(a)| < ε. Show more…
Show all steps
Your feedback will help us improve your experience
Andrew Noble and 65 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Write a delta-epsilon proof that shows that the function $f(x)=3 x-5$ is continuous at $x=2$.
Limits
Continuity and Its Consequences
Prove the statement using the $\varepsilon, \delta$ definition of limit. $\lim _{x \rightarrow 3} \frac{x}{5}=\frac{3}{5}$
Limits and Derivatives
The Precise Definition of a Limit
Write a delta-epsilon proof that shows that the function $f(x)=2 x+1$ is continuous at $x=5 .$ (This exercise depends on Section 1.3.)
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Watch the video solution with this free unlock.
EMAIL
PASSWORD