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We want to calculate: f(x) In |x|dx where: f(x) = 2x²-3-x+3 (x+4) a. Define F(z) = f(z)In(z), where In is defined by choosing arg(z) to lie between -a/2 and 3x/2. Then F(z) can be integrated along the contour as shown. The contour I where y, is a semicircular arc of radius R and y, is a semicircular arc of radius . What is the value of the contour integral r F(z)dz if & > 0 is very small and R > 0 is very large? f F(z)dz =

We want to calculate: f(x) In |x|dx where: f(x) = 2x²-3-x+3 (x+4) a. Define F(z) = f(z)In(z), where In is defined by choosing arg(z) to lie between -a/2 and 3x/2. Then F(z) can be integrated along the contour as shown. The contour I where y, is a semicircular arc of radius R and y, is a semicircular arc of radius . What is the value of the contour integral r F(z)dz if & > 0 is very small and R > 0 is very large? f F(z)dz =

Intermediate Algebra
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Conic Sections
Section8.2: More Parabolas And Some Circles
Problem 63.1PS
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We want to calculate: f(x) In |x|dx 2.x-3-x+3 (x*+4)? where: f(x) = a. Define F(z) = f(z) In(z), where In is defined by choosing arg(z) to lie between -a/2 and 3x/2. Then F(z) can be integrated along the contour r as shown. 2--R The contour I where y, is a semicircular arc of radius R and y, is a semicircular arc of radius d. What is the value of the contour integral r F(z)dz if i > 0 is very small andR > 0 is very large? F(z)dz = b. The integral , F(z)dz tends to zero as R → o because on y2 [choose ALL that are correct]: O|F(z)| is bounded by a constant multiple of R-2 for large Rand we can apply the standard integral bound. Owe can apply Jordan's Lemma. O|F(z)| is bounded by a constant multiple of-for large Rand we can apply the standard integral bound. O|F(z)| is bounded by a constant multiple of for large Rand we can apply the standard integral bound. c. The integral . F(z)dz tends to zero as ô 0 because on Y4 [choose ALL that are correct]: O |F(z)| is bounded and we can apply the standard integral bound. O we can apply Jordan's Lemma. O|F(z)| is bounded by a constant multiple of - for small positive ổ and we can apply the standard integral bound. O|F(z)| is bounded by a constant multiple of for small positive ô and we can apply the standard integral bound. d. Give the value of: I = [ f(x) In |x|dx
Transcribed Image Text:We want to calculate: f(x) In |x|dx 2.x-3-x+3 (x*+4)? where: f(x) = a. Define F(z) = f(z) In(z), where In is defined by choosing arg(z) to lie between -a/2 and 3x/2. Then F(z) can be integrated along the contour r as shown. 2--R The contour I where y, is a semicircular arc of radius R and y, is a semicircular arc of radius d. What is the value of the contour integral r F(z)dz if i > 0 is very small andR > 0 is very large? F(z)dz = b. The integral , F(z)dz tends to zero as R → o because on y2 [choose ALL that are correct]: O|F(z)| is bounded by a constant multiple of R-2 for large Rand we can apply the standard integral bound. Owe can apply Jordan's Lemma. O|F(z)| is bounded by a constant multiple of-for large Rand we can apply the standard integral bound. O|F(z)| is bounded by a constant multiple of for large Rand we can apply the standard integral bound. c. The integral . F(z)dz tends to zero as ô 0 because on Y4 [choose ALL that are correct]: O |F(z)| is bounded and we can apply the standard integral bound. O we can apply Jordan's Lemma. O|F(z)| is bounded by a constant multiple of - for small positive ổ and we can apply the standard integral bound. O|F(z)| is bounded by a constant multiple of for small positive ô and we can apply the standard integral bound. d. Give the value of: I = [ f(x) In |x|dx
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