11.3.2 Given n 2 3 lines in the plane in general position (no two are parallel and no three go through a point), prove that among the regions they divide the plane into, there is at least one triangle.
11.3.2 Given n 2 3 lines in the plane in general position (no two are parallel and no three go through a point), prove that among the regions they divide the plane into, there is at least one triangle.
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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Question
![f(x) is a cubic function with the leading coefficient of 1,
and for the positive value of “a,"
g(x) = f[f'(t +a) · f'(t − a)]dt and satisfying,
1/2
g(x) has extreme values only at x =
and x =
131323
2
If f (0) is -, what is the value of "a" multiplied by ƒ (1)?
2'](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb293512b-b0cd-4cf3-ac5f-0961bc4902d0%2F7ee17d22-a547-4f67-81b9-a0363ad1ea67%2Ffxbl9ch_processed.jpeg&w=3840&q=75)
Transcribed Image Text:f(x) is a cubic function with the leading coefficient of 1,
and for the positive value of “a,"
g(x) = f[f'(t +a) · f'(t − a)]dt and satisfying,
1/2
g(x) has extreme values only at x =
and x =
131323
2
If f (0) is -, what is the value of "a" multiplied by ƒ (1)?
2'
Transcribed Image Text:11.3.2 Given n 2 3 lines in the plane in general position (no two are parallel
and no three go through a point), prove that among the regions they divide the
plane into, there is at least one triangle.
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