1.- Use Laplace's method to obtain an asymtpotic expansion valid for x → ∞ of the complementary error function erfc(x) = 2/17√ √ p°³° ՐՁ e -t2 dt = 2 -x2 e S -2tx-t2 e e dt, (Note the Compare the asymp- totic results with the exact values erfc(2) = 0.004677735... and erfc(4) = 0.00000 00154 173.... Is the asymptotic expansion convergent? [Hints: Note that the function -2t (which is part of the exponent in the exponential e in the second integral above) has its maximum at an endpoint of the integration interval. Expand exp (-2) in a power series around the origin.] -2tx

1.- Use Laplace's method to obtain an asymtpotic expansion valid for x → ∞ of the complementary error function erfc(x) = 2/17√ √ p°³° ՐՁ e -t2 dt = 2 -x2 e S -2tx-t2 e e dt, (Note the Compare the asymp- totic results with the exact values erfc(2) = 0.004677735... and erfc(4) = 0.00000 00154 173.... Is the asymptotic expansion convergent? [Hints: Note that the function -2t (which is part of the exponent in the exponential e in the second integral above) has its maximum at an endpoint of the integration interval. Expand exp (-2) in a power series around the origin.] -2tx

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter9: Polynomial And Rational Functions

Section9.2: Remainder And Factor Theorems

Problem 51PS

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