# OC86656

## University of Toronto Scarborough

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## MAT223H1 Study Guide - Midterm Guide: Asymptote

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November 1, 2006, 8:30 9:20 a. m. family name given name (please print) student number. Instructions: do not open this booklet until told to do so, wri

View Document## MAT223H1 Study Guide - Midterm Guide: Riemann Sum, Maxima And Minima, Antiderivative

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Instructors: m. bays, d. haskell, e. harper, c. mclean. This test paper is printed on both sides of the page. You are responsible for ensuring that you

View Document## MAT223H1 Study Guide - Midterm Guide: Parametric Equation, Trapezoidal Rule, Farad

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Instructions: do not open this booklet until. Told to do so: fill in the above box, this exam contains 7 pages with a total of. /30: compute the follow

View Document## Simon Fraser MATH 150 Nov 2005 Midterm 2

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@sfu. ca: do not lift up the cover page until instructed, circle your instructor. If you don"t, you lose a mark: this test is comprised of 8 pages, onc

View Document## MAT136H1 Lecture Notes - Antiderivative

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Question #5 (medium): using series to approximate definite integral. Same as evaluating the indefinite integral, definite integral follows the same pro

View Document## MAT136H1 Lecture Notes - Ratio Test

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Question #3 (medium): maclaurin series and radius of convergence. There is a handful number of equations for ( ) ( ) which can readily used. For any de

View Document## MAT136H1 Lecture Notes - Ratio Test

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Question #1 (easy): maclaurin series and radius of convergence. Maclaurin series is exactly same as taylor series of the function at , but where. Find

View Document## MAT136H1 Lecture Notes - Ratio Test

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Question #2 (medium): taylor series and its radius of convergence. Radius of convergence is determined using the ratio test | So any value of that make

View Document## MAT136H1 Lecture Notes - Antiderivative

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Question #4 (medium): evaluating indefinite integral as infinite series. Any given function inside the indefinite integral can be expressed as a infini

View Document## MAT136H1 Lecture Notes - Partial Fraction Decomposition, Partial Function

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Question #2 (medium): interval of convergence for partial fraction function. For partial fractions, consider each partial fraction as a separate geomet

View Document## MAT136H1 Lecture Notes - Geometric Series

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Question #1 (easy): representing function into power series. To convert the function into a power series, first think of geometric series whose sum is

View Document## 11.9 Function Representation as Power Series Question #5 (Medium)

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Question #5 (medium): definite integral approximation using power series. Power series representation of the definite integral can be used to approxima

View Document## 11.8 Power Series Overview

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Where "s are coefficients and is a variable. Power series: overview looks like polynomial, except with infinite terms. 3 possibilities: series converge

View Document## MAT136H1 Lecture Notes - Ratio Test

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Question #2 (medium): radius and interval of convergence for power series. To get the radius of convergence, first put the series expression into the r

View Document## MAT136H1 Lecture Notes - Absolute Convergence, Alternating Series Test, Integral Test For Convergence

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Question #1 (easy): determining the radius and interval of convergence. Power series contain variable in the series expression so that where "s are coe

View Document## MAT136H1 Study Guide - Midterm Guide: Ratio Test, Alternating Series, Conditional Convergence

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Question #3 (medium): alternating series tested using the ratio test. | means is divergent is absolutely convergent (ie. convergent) | means no conclus

View Document## MAT136H1 Study Guide - Midterm Guide: Ratio Test, Conditional Convergence

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By the word ratio test, it takes and the next term expression and takes a ratio of the two so that: | means is absolutely convergent (ie. convergent) |

View Document## MAT136H1 Study Guide - Midterm Guide: Conditional Convergence, Root Test

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, or means means is absolutely convergent (ie. convergent) is divergent means no conclusion can be drawn from the root test about convergence or diverg

View Document## MAT136H1 Lecture Notes - Alternating Series Test, Alternating Series

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Question #3 (medium): number of terms in the series needed to meet the error bound. Alternating series test states that the series converges if it meet

View Document## MAT136H1 Lecture Notes - Alternating Series Test, Alternating Series

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Question #5 (medium): making the alternating series convergent. To find the missing variable to make the alternating series convergent, keep the missin

View Document## MAT136H1 Lecture Notes - Alternating Series Test, Alternating Series

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Question #2 (medium): converging series against alternating series test. Alternating series test states that the series converges if it meets two condi

View Document## MAT136H1 Lecture Notes - Alternating Series

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Question #4 (medium): sum of series correct to limited decimal place. In order to determine the sum of the series exactly correct to the number of deci

View Document## 11.4 Comparison Tests Question #2 (Medium)

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The key is to come up with a much simpler function that is obvious as to whether is it convergent or divergent. Then comparing to this simpler function

View Document## MAT136H1 Study Guide - Midterm Guide: Limit Comparison Test

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Limit comparison test states that for series with positive terms and , if for a finite number , then both series converge or both series diverge. So se

View Document## MAT136H1 Study Guide - Midterm Guide: Improper Integral

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Question #4 (medium): estimating the sum of series and its error. Based on the first n number of terms in the series, the sum can be estimated. The err

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