5. Consider the functions et - e-* et + e-* a(x) = and B(x) = In this question, you may freely use the fact that B² (x) – a² (x) = 1. Verify that a'(x) = B(x) and B'(x) = a(x). (ii) of a-1. Simplify as much as possible, using the fact that 32 (x) - a2 (x) = 1 to write your answer without any a's or B's. The function a is invertible. Use the Inverse Function Theorem to compute the derivative The inverse of a can be explicitly computed to be a-'(x) = lIn(x + /x² + 1). Compute (ii) the derivative of a-1 (this time without using the Inverse Function Theorem) and confirm that you get the same answer as part (ii).

5. Consider the functions et - e-* et + e-* a(x) = and B(x) = In this question, you may freely use the fact that B² (x) – a² (x) = 1. Verify that a'(x) = B(x) and B'(x) = a(x). (ii) of a-1. Simplify as much as possible, using the fact that 32 (x) - a2 (x) = 1 to write your answer without any a's or B's. The function a is invertible. Use the Inverse Function Theorem to compute the derivative The inverse of a can be explicitly computed to be a-'(x) = lIn(x + /x² + 1). Compute (ii) the derivative of a-1 (this time without using the Inverse Function Theorem) and confirm that you get the same answer as part (ii).

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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