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-5 Kilometers from poiint of secondary contact (x) Figure 1: The hybrid index in the warblers (see right hand photo). The vertical dashed line indicates a longitude of 123 deg (longitude=indicates location on the east/west axes of the earth). Vancouver B.C. has a longitude of 123 deg Where hybrid index H as a function of distance r is given by: 2e (1 – e") H(x) : (1+e*)² (1) A. Identify where in the plot the first derivative is 0 B. Fill in the blanks to find the first derivative of H(x) with respect to x. Applying the quotient rule we have: [(1+e*)°# (e=/2(1– e*)) – e=/?(1- (1+ e")4 )#(1+e*)°] dH(x) dx 'Dr. Silu Wang is an amazing nature photographer and artist. Check out her work on instagram. 1

-5 Kilometers from poiint of secondary contact (x) Figure 1: The hybrid index in the warblers (see right hand photo). The vertical dashed line indicates a longitude of 123 deg (longitude=indicates location on the east/west axes of the earth). Vancouver B.C. has a longitude of 123 deg Where hybrid index H as a function of distance r is given by: 2e (1 – e") H(x) : (1+e*)² (1) A. Identify where in the plot the first derivative is 0 B. Fill in the blanks to find the first derivative of H(x) with respect to x. Applying the quotient rule we have: [(1+e*)°# (e=/2(1– e*)) – e=/?(1- (1+ e")4 )#(1+e*)°] dH(x) dx 'Dr. Silu Wang is an amazing nature photographer and artist. Check out her work on instagram. 1

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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Student Name (#): IQ7 Problem 1: The tension zone Dr. Silu Wang ' studies hybrid birds in the Pacific Northwest. One of the interesting things about birds in Washington state and BC is that 20,000 years ago glaciers covered much of BC. As the glaciers melted birds once living on Haida Gwaii, which was never covered in ice, spread across BC and then came into "secondary contact" and bred with birds from the Midwestern United States. Dr. Wang measures genetically whether birds are western like (a positive hybrid index) or eastern like (a negative hybrid index). Sampling birds from across Washington, she observed the following approximate pattern of the hybrid index. 0.4 0.2 0.0 -0.2 -0.4 -5 5 Kilometers from poiint of secondary contact (x) Figure 1: The hybrid index in the warblers (see right hand photo). The vertical dashed line indicates a longitude of 123 deg (longitude=indicates location on the east/west axes of the earth). Vancouver B.C. has a longitude of 123 deg Where hybrid index H as a function of distance x is given by: 2e2 (1 – e) H(x) = (1) (1+ e*)² A. Identify where in the plot the first derivative is 0 B. Fill in the blanks to find the first derivative of H(x) with respect to x. Applying the quotient rule we have: (1+e*)² & – e"/²(1 – e") (1+ e")? e#/2(1 – d (e"/2(1 – e")) (1+ ea)4 d dH (х) x\2 dx 1 – e") (1+ e")² dx (2) dx 'Dr. Silu Wang is an amazing nature photographer and artist. Check out her work on instagram. 1 Hybrid Index
Transcribed Image Text:Student Name (#): IQ7 Problem 1: The tension zone Dr. Silu Wang ' studies hybrid birds in the Pacific Northwest. One of the interesting things about birds in Washington state and BC is that 20,000 years ago glaciers covered much of BC. As the glaciers melted birds once living on Haida Gwaii, which was never covered in ice, spread across BC and then came into "secondary contact" and bred with birds from the Midwestern United States. Dr. Wang measures genetically whether birds are western like (a positive hybrid index) or eastern like (a negative hybrid index). Sampling birds from across Washington, she observed the following approximate pattern of the hybrid index. 0.4 0.2 0.0 -0.2 -0.4 -5 5 Kilometers from poiint of secondary contact (x) Figure 1: The hybrid index in the warblers (see right hand photo). The vertical dashed line indicates a longitude of 123 deg (longitude=indicates location on the east/west axes of the earth). Vancouver B.C. has a longitude of 123 deg Where hybrid index H as a function of distance x is given by: 2e2 (1 – e) H(x) = (1) (1+ e*)² A. Identify where in the plot the first derivative is 0 B. Fill in the blanks to find the first derivative of H(x) with respect to x. Applying the quotient rule we have: (1+e*)² & – e"/²(1 – e") (1+ e")? e#/2(1 – d (e"/2(1 – e")) (1+ ea)4 d dH (х) x\2 dx 1 – e") (1+ e")² dx (2) dx 'Dr. Silu Wang is an amazing nature photographer and artist. Check out her work on instagram. 1 Hybrid Index
de (e2(1 – e")) = Evaluate the following two derivatives: d (3) d (1+ e*)². dx Simplifying gives: dH(x) e#/2 (e2a 6et + 1) (4) dx (1+ e*)3 C. Given that: &H(x) ea/2 (23e" – 23e2 2 (e* + 1)* + e3* – 1) (5) dx? Evaluate the sign of the second derivative at every integer between -6 and 6 -6 -5 -4 -3 -2 -1 1 sign () d? H dx2 D. What does the sign of the second derivative represent? E. Does your answer to C match the graph? 2.
Transcribed Image Text:de (e2(1 – e")) = Evaluate the following two derivatives: d (3) d (1+ e*)². dx Simplifying gives: dH(x) e#/2 (e2a 6et + 1) (4) dx (1+ e*)3 C. Given that: &H(x) ea/2 (23e" – 23e2 2 (e* + 1)* + e3* – 1) (5) dx? Evaluate the sign of the second derivative at every integer between -6 and 6 -6 -5 -4 -3 -2 -1 1 sign () d? H dx2 D. What does the sign of the second derivative represent? E. Does your answer to C match the graph? 2.
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