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On Parametrization: Show that a half circle in the upper half plane with radius R and centered at origin can be parametrized in various ways as given below: a. x(t) = R cost, y(t) = R sint; where 0

On Parametrization: Show that a half circle in the upper half plane with radius R and centered at origin can be parametrized in various ways as given below: a. x(t) = R cost, y(t) = R sint; where 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. On Parametrization: Show that a half circle in the upper half plane with radius R and centered at origin can be parametrized in various ways as given below: a. x(t) = R cost, y(t) = R sint; where 0<t<n b. x(t) = t, y(t) = √R²-t²; where - R < t < R c. x(t) = R(2t - 1), y(t) = 2R√t-t²; where0 < t < 1 2. On Simple Contour Integrals:
Transcribed Image Text:1. On Parametrization: Show that a half circle in the upper half plane with radius R and centered at origin can be parametrized in various ways as given below: a. x(t) = R cost, y(t) = R sint; where 0<t<n b. x(t) = t, y(t) = √R²-t²; where - R < t < R c. x(t) = R(2t - 1), y(t) = 2R√t-t²; where0 < t < 1 2. On Simple Contour Integrals:
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