Suppose that (x) satisfies the following equation (an example of a differential equation) (a) Show that (x) 2 '(x) 2 (0) 2 '(0) 2 for all x Show that the function on the left has zero derivative (b) Verify that sin x and cos x satisfy Eq (1), and deduce that sin 2 x cos 2 x 1 Eq (1) f (x) f(x)...

a Let gx fx fx Then gx 2fxfx 2fxfx 2fxfx 2fxfx 0 where we ...

Suppose that (x) satisfies the following equation (an example of a differential equation): (a) Show that (x)

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Suppose that ƒ(x) satisfies the following equation (an example of a differential equation):

(a) Show that ƒ(x)²+ ƒ'(x)²= ƒ(0)²+ ƒ'(0)²for all x. Show that the function on the left has zero derivative.
(b) Verify that sin x and cos x satisfy Eq. (1), and deduce that sin² x + cos²x = 1.

Eq.(1)

f'(c) = f(b)-f(a) b-a

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Nov 15, 2023 07:07 AM

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Suppose that (x) satisfies the following equation (an example of a differential equation): (a) Show that (x)

Question:

f"(x) = -f(x)

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a Let gx fx fx Then gx 2fxfx 2fxfx 2fxfx 2fxfx 0 where we ...View the full answer

Calculus

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