When we take the derivative of f (x) = sin(x) cot(x) we will find f' (æ) = – sin(x). However, we must consider that the given function f (x) is not defined for all real values of x. • This is because cot(x) cos(z) sin(z) is undefined when sin(x) = 0. Fact to Recall, and new terminology When f is undefined at a certain value of æ, then f' is also undefined at that same value of æ. This idea is called "restrictions on the domain." Question The derivative f' (x) equals – sin(x), except at a few values where it is undefined (restrictions on the domain). What are the restrictions on the domain? O f' (x) is undefined for æ = 0, , -, 7, –7, , -, 27, –27, , -... O f' (x) is undefined for æ = .0, 플, -졸, 플, -플, 똘, -똘, 5x 2 o f (г) is undefined for a 0, п, —п, 2т, -2п, Зп, —Зп, ...
When we take the derivative of f (x) = sin(x) cot(x) we will find f' (æ) = – sin(x). However, we must consider that the given function f (x) is not defined for all real values of x. • This is because cot(x) cos(z) sin(z) is undefined when sin(x) = 0. Fact to Recall, and new terminology When f is undefined at a certain value of æ, then f' is also undefined at that same value of æ. This idea is called "restrictions on the domain." Question The derivative f' (x) equals – sin(x), except at a few values where it is undefined (restrictions on the domain). What are the restrictions on the domain? O f' (x) is undefined for æ = 0, , -, 7, –7, , -, 27, –27, , -... O f' (x) is undefined for æ = .0, 플, -졸, 플, -플, 똘, -똘, 5x 2 o f (г) is undefined for a 0, п, —п, 2т, -2п, Зп, —Зп, ...
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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Transcribed Image Text:When we take the derivative of ƒ (x)= sin(x) cot(x) we will find
f' (x) = – sin(x).
However, we must consider that the given function f (x) is not defined for all real values of x.
• This is because cot(x) :
cos(x)
sin(x)
is undefined when sin(x) = 0.
Fact to Recall, and new terminology
*When f is undefined at a certain value of æ, then f' is also undefined at that same value of æ.
This idea is called "restrictions on the domain."
Question
The derivative f' (x) equals – sin(x), except at a few values where it is undefined (restrictions on the domain).
What are the restrictions on the domain?
O f' (x) is undefined for x = 0, 5, -, 7, -n, , -, 27, –27, , -
2
O f' (æ) is undefined for æ = 0, 5, -5,5, -5, , -,...
2
2: 2 >
2 2
o ff («) is undefined for a- 0, п, —п, 2т, —2п, Зп, —Зп, ...
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