devry math260 week 1 and week 2 discussions latest 2015

Understanding Limits and Derivatives (graded)

This week, we will be dealing with limits and their connection to the derivative. Here are some questions that we will address. Please post your answers in this thread.

What is a limit?

How is the mathematical meaning of a limit similar to and different from how we perceive a limit in the real world?

How do we find a limit?

Under what circumstances is a limit undefined?

How does continuity play a role in finding limits and vice versa?

Discuss the continuity of the following: f(x) = (x + 3)/(x^2 - 9).

How do limits play a role in exploring vertical and horizontal asymptotes?

How are one-sided and two-sided limits related? How can the relation sometimes be used to determine the existence or nonexistence of a limit?

How can the answers to these questions help us link the concept of limit to the concept of derivative?

What is the limit definition of derivative? How can we use it to find a derivative?

Please feel free to use examples from the homework to illustrate your answers.

week 2

This week, we will be exploring the concept of derivative. Here are some questions that we will address. Please post your answers in this thread.

• What is the derivative? Mathematically and/or real world?
• What is the power rule and how do we use it to find a derivative?
• What is the product rule and how do we use it to find a derivative?
• What is the quotient rule and how do we use it to find a derivative?
• What is the chain rule and how do we use it to find a derivative?
• What information can be obtained from derivatives?
• Please provide an example from the real world and explain the information that you could gain from it.
• How do we find higher-order derivatives?
• How are the higher-order derivatives for f(x) = 3x⁶ different from the higher-order derivatives of f(x) = 2x-4? Please use examples from the homework to illustrate your answers.