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5. Consider the functions e a(z) and B(z) = . e +e 2 In this question, you may freely use the fact that 82(z) – a (z) = 1. (i) Verify that a'(z) = 3(2) and B'(x) = a(r). S The function a is invertible. Use the Inverse Function Theorem to compute the derivative of a1. Simplify as much as possible, using the fact that 82(r) - a (x) = 1 to write your answer without any a's or B's. (iii) the derivative of a- (this time without using the Inverse Function Theorem) and confirm that you get the same answer as part (ii). (ii) ) The inverse of a can be explicitly computed to be a-(2) = In(r + Vr? + 1). Compute

5. Consider the functions e a(z) and B(z) = . e +e 2 In this question, you may freely use the fact that 82(z) – a (z) = 1. (i) Verify that a'(z) = 3(2) and B'(x) = a(r). S The function a is invertible. Use the Inverse Function Theorem to compute the derivative of a1. Simplify as much as possible, using the fact that 82(r) - a (x) = 1 to write your answer without any a's or B's. (iii) the derivative of a- (this time without using the Inverse Function Theorem) and confirm that you get the same answer as part (ii). (ii) ) The inverse of a can be explicitly computed to be a-(2) = In(r + Vr? + 1). Compute

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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there is only one question so kinldy have a look and solve all parts of q5 in one hour only plz don't take too much time and take a thumb up plz
5. Consider the functions e +e a(x) = and B(1) = 2 2 In this question, you may freely use the fact that 8(z) – a (r) = 1. Verify that a'(z) = B(x) and B'(x) = a(r). The function a is invertible. Use the Inverse Function Theorem to compute the derivative (i) (ii) of a1. Simplify as much as possible, using the fact that B2(x)- a (x) = 1 to write your answer without any a's or B's. (iii) the derivative of a" (this time without using the Inverse Function Theorem) and confirm that you get the same answer as part (ii). ) The inverse of a can be explicitly computed to be a-() = In(x+ vr? +1). Compute
Transcribed Image Text:5. Consider the functions e +e a(x) = and B(1) = 2 2 In this question, you may freely use the fact that 8(z) – a (r) = 1. Verify that a'(z) = B(x) and B'(x) = a(r). The function a is invertible. Use the Inverse Function Theorem to compute the derivative (i) (ii) of a1. Simplify as much as possible, using the fact that B2(x)- a (x) = 1 to write your answer without any a's or B's. (iii) the derivative of a" (this time without using the Inverse Function Theorem) and confirm that you get the same answer as part (ii). ) The inverse of a can be explicitly computed to be a-() = In(x+ vr? +1). Compute
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