Pls help ASAP 5. Consider the functionsa(x) =e - e-and B(x) =e +e-z%3D%3DIn this question, you may freely use the fact that 82(x)- a²(x) = 1.= 1.(i)Verify that a' (x) = B(x) and B'(x) = a(z).The function a is invertible. Use the Inverse Function Theorem to compute the derivative%3D(ii)of a. Simplify as much as possible, using the fact that 82(x) - a2(x) = 1 to write your answerwithout any a's or B's.(iii)the derivative of a (this time without using the Inverse Function Theorem) and confirm that youget the same answer as part (ii).The inverse of a can be explicitly computed to be a(r) = In(x+ v + 1). Compute%3D

Inverse function theorem If f is invertible function then f-1x'= 1f'f-1x

Consider the functions a(z) and B(x) = e +e- In this question, you may freely use the fact that 8 (x)- a (x) = 1. (i) %3D Verify that a'(r) = B(r) and B'(r) = a(r). The function a is invertible. Use the Inverse Function Theorem to compute the derivative (ii) of a Simplify as much as possible, using the fact that B2(x) – a (r) =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(x) = In(r+ v + 1). Compute %3D

Consider the functions a(z) and B(x) = e +e- In this question, you may freely use the fact that 8 (x)- a (x) = 1. (i) %3D Verify that a'(r) = B(r) and B'(r) = a(r). The function a is invertible. Use the Inverse Function Theorem to compute the derivative (ii) of a Simplify as much as possible, using the fact that B2(x) – a (r) =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(x) = In(r+ v + 1). Compute %3D

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

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