(a) Suppose f is a function with domain the interval (a, b) with a < b. If f is an even function, what can be deduced about the connection between a and b? (b) (i) Give an example of an even function whose domain has exactly four elements. (ii) Give an example of an odd function whose domain has exactly three elements
(a) Suppose f is a function with domain the interval (a, b) with a < b. If f is an even function, what can be deduced about the connection between a and b? (b) (i) Give an example of an even function whose domain has exactly four elements. (ii) Give an example of an odd function whose domain has exactly three elements
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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- (a) Suppose f is a function with domain the interval (a, b) with a < b. If f is an even function,
what can be deduced about the connection between a and b?
(b) (i) Give an example of an even function whose domain has exactly four elements.
(ii) Give an example of an odd function whose domain has exactly three elements
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(u) Dtate Ule precise reasoll W Ily J IS CONUIIIUOUS al 2.
sin 4.x
if x > 0
3. Suppose f(x) =
if x = 0. Find f'(0) using the definition of derivatives.
„2
x + 4x
if x < 0
4. Find the derivatives of the following functions. Do not simplify your answer!
d.
(a)
dx Vx² + 1
sec x
d
(b)
[2° (x² + 1)° tan a ]
dx
d
(c) sin ()
5
dx
x +1
d
(d)
cos(x³ cos r³)
dx
5. Sketch the graph of a function f with domain [1,5] satisfying all the following conditions:
• continuous on [1,5);
discontinuous at 5 from the left;
has only one local maximum at 4;
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(u) Dtate Ule precise reasoll W Ily J IS CONUIIIUOUS al 2.
sin 4.x
if x > 0
3. Suppose f(x) =
if x = 0. Find f'(0) using the definition of derivatives.
„2
x + 4x
if x < 0
4. Find the derivatives of the following functions. Do not simplify your answer!
d.
(a)
dx Vx² + 1
sec x
d
(b)
[2° (x² + 1)° tan a ]
dx
d
(c) sin ()
5
dx
x +1
d
(d)
cos(x³ cos r³)
dx
5. Sketch the graph of a function f with domain [1,5] satisfying all the following conditions:
• continuous on [1,5);
discontinuous at 5 from the left;
has only one local maximum at 4;
88
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)
at N a H O ở O
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