Category Archives: Approximation

Taylor Series

0. Can we approximate a function using a power series? With the calculus’ help, we can! Advertisements

Posted in Analysis, Approximation, Calculus, Differential, Infinite Series, Power Series, Taylor Series | Tagged , | 3 Comments

Integral Test for Convergence

1. So we have the definition for a series to converge, but what about some slick tests? Wait a moment: wasn’t a Riemann Sum an infinite series? Why don’t we use integration to test if a series converges or diverges? … Continue reading

Posted in Analysis, Approximation, Calculus, Infinite Series | Leave a comment

Example Riemann Sums

1. Introduction. There are different ways to do the Riemann Sum. What I mean is, recall the definition for the Riemann sum looked like for some . There are many different choices for , but three are most popular: 1. … Continue reading

Posted in Approximation, Calculus, Integral, Riemann Integral | 2 Comments

Curve Sketching (General Scheme)

1. First Attempt. We have some complicated function, and we want to graph it…but don’t have a calculator, computer, cell phone, etc. What do we do? Lets fix our notation now. We are trying to sketch the curve of . … Continue reading

Posted in Approximation, Curve Sketching | 2 Comments

Tangent Lines as Linear Approximations

1. Motivation. So we have some procedure to construct a line tangent to a curve at a given point. What good is it? Well, suppose we want to compute . What is it? I don’t know! Lets introduce the function … Continue reading

Posted in Approximation, Calculus, Differential, Tangent Line | Tagged | 4 Comments