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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 Power Series, Taylor Series
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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
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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
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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
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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