Note:Please provide a detailed, step-by-step solution. It’s essential to double-check the entire solution to avoid any mistakes. I request handwritten working out, as it helps with clarity and understanding. Additionally, carefully review the image for conceptual understanding and ensure that no relevant details are missed.I’ve noticed that I often receive incorrect answers, so it’s crucial that you thoroughly go through the question and solution process, step by step, before finalizing. I truly appreciate your time and meticulous attention to detail.Everything is in the image for clarity!. Thanks again, for your time!. 2. Let C be the vector space of continuous functions and let V be the subspace spanned by the setE={cos(x), sin(x), cos(2x), sin(2x)}.Consider the linear transformation T : VV defined by T(f(x)) = f'(x), sending a function f(x) = V toits derivative.(a) Show that Ɛ is a basis for V.Hint: Plug in x = 0, π/2, π.(b) Find the matrix [T] of the transformation T with respect to the basis ε.(c) Show that [T] is a diagonal matrix.(d) Describe the linear transformation represented by the matrix [T]. That is, give L(f(x)) for the lineartransformation LVV with [L] = [T].[1234]-5(e) Suppose f(x) = V has coordinates [f(x)] =with respect to the basis Ɛ. Compute the 100thπderivative of f. Your answer should be an element of V.

2. Let C be the vector space of continuous functions and let V be the subspace spanned by the set E={cos(x), sin(x), cos(2x), sin(2x)}. Consider the linear transformation T : VV defined by T(f(x)) = f'(x), sending a function f(x) = V to its derivative. (a) Show that Ɛ is a basis for V. Hint: Plug in x = 0, π/2, π. (b) Find the matrix [T] of the transformation T with respect to the basis ε. (c) Show that [T] is a diagonal matrix. (d) Describe the linear transformation represented by the matrix [T]. That is, give L(f(x)) for the linear transformation LVV with [L] = [T]. [1234] -5 (e) Suppose f(x) = V has coordinates [f(x)] = with respect to the basis Ɛ. Compute the 100th π derivative of f. Your answer should be an element of V.

2. Let C be the vector space of continuous functions and let V be the subspace spanned by the set E={cos(x), sin(x), cos(2x), sin(2x)}. Consider the linear transformation T : VV defined by T(f(x)) = f'(x), sending a function f(x) = V to its derivative. (a) Show that Ɛ is a basis for V. Hint: Plug in x = 0, π/2, π. (b) Find the matrix [T] of the transformation T with respect to the basis ε. (c) Show that [T] is a diagonal matrix. (d) Describe the linear transformation represented by the matrix [T]. That is, give L(f(x)) for the linear transformation LVV with [L] = [T]. [1234] -5 (e) Suppose f(x) = V has coordinates [f(x)] = with respect to the basis Ɛ. Compute the 100th π derivative of f. Your answer should be an element of V.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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