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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![1. Let / be the function given by f(x)= 3x - 5. Use the contrapositive implication to prove:
If x₂ * x₂, then f(x₁) = f(x₂).
2. Prove that for every
>0 there exists a 5>0 such that
1-6 <x< 1+8 implies 5-<2x+3<5+ e
3. For every real number x > 3, there exists a real number y < 0 such that x =
4. If x²+x-620, then x S-3 or x 22.
5. Fill in the blanks in the proof of the following theorem.
Theorem: ASB iff AUB=B.
Proof: Suppose that ASB. If x E AUB, then x € A or x E
Since AS B, in either case we have x E B. Thus,
On the other hand if x Ethen x E AUB, so
Hence, AUB=B.
Conversely, suppose that A UB= B. If x E A, then x E
Thus
But AUB=B, so xe_
6. Find Use B and Nae B for each collection 3.
a. 3- ={[1.1+]:EN]
-{(1.1+)neN)
c. 3=([0,3]. (1,5),(2,4))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd1669fa-bea5-4ae8-bcbe-d4dcbcb5b1f8%2F72ccdcce-98f6-4694-9929-728d0cb3c9a1%2Ffmgwugq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Let / be the function given by f(x)= 3x - 5. Use the contrapositive implication to prove:
If x₂ * x₂, then f(x₁) = f(x₂).
2. Prove that for every
>0 there exists a 5>0 such that
1-6 <x< 1+8 implies 5-<2x+3<5+ e
3. For every real number x > 3, there exists a real number y < 0 such that x =
4. If x²+x-620, then x S-3 or x 22.
5. Fill in the blanks in the proof of the following theorem.
Theorem: ASB iff AUB=B.
Proof: Suppose that ASB. If x E AUB, then x € A or x E
Since AS B, in either case we have x E B. Thus,
On the other hand if x Ethen x E AUB, so
Hence, AUB=B.
Conversely, suppose that A UB= B. If x E A, then x E
Thus
But AUB=B, so xe_
6. Find Use B and Nae B for each collection 3.
a. 3- ={[1.1+]:EN]
-{(1.1+)neN)
c. 3=([0,3]. (1,5),(2,4))
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