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Exercise 1.1: For the function f(x) = sin(x) in the domain (0, π), (a) Sketch the function f(x) in the domain specified above. (b) What is the value of f(0) and ƒ(π). (c) What is the value of c such that f(c) = 0 ? Your answer should confirm that 0

Exercise 1.1: For the function f(x) = sin(x) in the domain (0, π), (a) Sketch the function f(x) in the domain specified above. (b) What is the value of f(0) and ƒ(π). (c) What is the value of c such that f(c) = 0 ? Your answer should confirm that 0

Advanced Engineering Mathematics
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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Theorem 1 (Rolle's Theorem) Suppose f is a continuous function in the domain (a, b). If f(a) = f(b) = 0, then a number c exist in (a, b) such that f'(c) = 0. This theorem is illustrated in Fig. 1.1. Exercise 1.1: For the function f(x) = sin(x) in the domain (0,7), (a) Sketch the function f(x) in the domain specified above. (b) What is the value of f(0) and f(T). (c) What is the value of c such that f(c) = 0 ? Your answer should confirm that 0 <C<T.
Transcribed Image Text:Theorem 1 (Rolle's Theorem) Suppose f is a continuous function in the domain (a, b). If f(a) = f(b) = 0, then a number c exist in (a, b) such that f'(c) = 0. This theorem is illustrated in Fig. 1.1. Exercise 1.1: For the function f(x) = sin(x) in the domain (0,7), (a) Sketch the function f(x) in the domain specified above. (b) What is the value of f(0) and f(T). (c) What is the value of c such that f(c) = 0 ? Your answer should confirm that 0 <C<T.
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