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A quick way to graph cos(x + h) – cos(x) is g(x) = lim h→0 h to graph which of the following?

A quick way to graph cos(x + h) – cos(x) is g(x) = lim h→0 h to graph which of the following?

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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A quick way to graph \[ g(x) = \lim_{h \to 0} \frac{\cos(x + h) - \cos(x)}{h} \] is to graph which of the following?
Transcribed Image Text:A quick way to graph \[ g(x) = \lim_{h \to 0} \frac{\cos(x + h) - \cos(x)}{h} \] is to graph which of the following?
### Mathematical Expressions for Trigonometric Functions Here are different expressions representing the function \( g(x) \): 1. **Expression**: \( g(x) = \sin x \) - Description: This is the sine function, which is periodic with a period of \(2\pi\). It oscillates between -1 and 1 and is an odd function. 2. **Expression**: \( g(x) = -\sin x \) - Description: This is the negative sine function. It mirrors the sine function across the x-axis, maintaining the same period and amplitude. 3. **Expression**: \( g(x) = \cos x \) - Description: This is the cosine function, also periodic with a period of \(2\pi\). It ranges from -1 to 1 and is an even function, starting at 1 when \(x = 0\). 4. **Expression**: \( g(x) = -\cos x \) - Description: This is the negative cosine function. It is a reflection of the cosine function across the x-axis, with identical period and amplitude characteristics.
Transcribed Image Text:### Mathematical Expressions for Trigonometric Functions Here are different expressions representing the function \( g(x) \): 1. **Expression**: \( g(x) = \sin x \) - Description: This is the sine function, which is periodic with a period of \(2\pi\). It oscillates between -1 and 1 and is an odd function. 2. **Expression**: \( g(x) = -\sin x \) - Description: This is the negative sine function. It mirrors the sine function across the x-axis, maintaining the same period and amplitude. 3. **Expression**: \( g(x) = \cos x \) - Description: This is the cosine function, also periodic with a period of \(2\pi\). It ranges from -1 to 1 and is an even function, starting at 1 when \(x = 0\). 4. **Expression**: \( g(x) = -\cos x \) - Description: This is the negative cosine function. It is a reflection of the cosine function across the x-axis, with identical period and amplitude characteristics.
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