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2. Suppose f (x) is a function whose domain is all real numbers, which satisfies the formula: f (x + y) = f (x) (sin (y) + 1) for any numbers x and y. (a) Show that f (x) is differentiable for all real numbers, and f' (x) = ƒ (x) for any x. (b) Can you think of an example of f (x) that satisfies the formula?

2. Suppose f (x) is a function whose domain is all real numbers, which satisfies the formula: f (x + y) = f (x) (sin (y) + 1) for any numbers x and y. (a) Show that f (x) is differentiable for all real numbers, and f' (x) = ƒ (x) for any x. (b) Can you think of an example of f (x) that satisfies the formula?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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2. Suppose f (x) is a function whose domain is all real numbers, which satisfies the formula: f (x + y) = f (x) (sin (y) + 1) for any numbers x and y. (a) Show that f (x) is differentiable for all real numbers, and f' (x) = ƒ (x) for any x. (b) Can you think of an example of f (x) that satisfies the formula?
Transcribed Image Text:2. Suppose f (x) is a function whose domain is all real numbers, which satisfies the formula: f (x + y) = f (x) (sin (y) + 1) for any numbers x and y. (a) Show that f (x) is differentiable for all real numbers, and f' (x) = ƒ (x) for any x. (b) Can you think of an example of f (x) that satisfies the formula?
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