Let R; = xER|1 < x < 1 + 1, 1 + for each positive integer i. (Enter your answers using interval notation.) = (a) U R; = [1,2] i = 1 (b) 9 10 n R; =| 1,- 9. i = 1
Let R; = xER|1 < x < 1 + 1, 1 + for each positive integer i. (Enter your answers using interval notation.) = (a) U R; = [1,2] i = 1 (b) 9 10 n R; =| 1,- 9. i = 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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how do i solve b
![### Understanding Intervals and Set Operations
Consider the set \(R_i\) defined by:
\[ R_i = \left\{ x \in \mathbb{R} \mid 1 \leq x \leq 1 + \frac{1}{i} \right\} = \left[ 1, 1 + \frac{1}{i} \right] \]
for each positive integer \(i\).
#### Task
Evaluate the following set operations using interval notation (provide answers where indicated):
### (a) Union of Sets
Find the union of \(R_i\) for \(i = 1\) to \(9\):
\[ \bigcup_{i=1}^9 R_i = \left[1, 2\right] \]
The provided answer is correct:
\[ \left[1, 2\right] \] ✅
### (b) Intersection of Sets
Find the intersection of \(R_i\) for \(i = 1\) to \(9\):
\[ \bigcap_{i=1}^9 R_i = \left[1, \frac{10}{9}\right] \]
The provided answer is incorrect:
\[ 1, \frac{10}{9} \] ❌
### Explanation of Graph or Diagram (if any)
There is no graph or diagram in the provided image, only mathematical notation and boxed answers with accompanying correctness indicators.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F507ffaff-36d6-4c89-a9b8-d054ae79319d%2F0f518e29-1d91-4c33-8d53-65ba44e2b8fe%2Fuhjk51e.png&w=3840&q=75)
Transcribed Image Text:### Understanding Intervals and Set Operations
Consider the set \(R_i\) defined by:
\[ R_i = \left\{ x \in \mathbb{R} \mid 1 \leq x \leq 1 + \frac{1}{i} \right\} = \left[ 1, 1 + \frac{1}{i} \right] \]
for each positive integer \(i\).
#### Task
Evaluate the following set operations using interval notation (provide answers where indicated):
### (a) Union of Sets
Find the union of \(R_i\) for \(i = 1\) to \(9\):
\[ \bigcup_{i=1}^9 R_i = \left[1, 2\right] \]
The provided answer is correct:
\[ \left[1, 2\right] \] ✅
### (b) Intersection of Sets
Find the intersection of \(R_i\) for \(i = 1\) to \(9\):
\[ \bigcap_{i=1}^9 R_i = \left[1, \frac{10}{9}\right] \]
The provided answer is incorrect:
\[ 1, \frac{10}{9} \] ❌
### Explanation of Graph or Diagram (if any)
There is no graph or diagram in the provided image, only mathematical notation and boxed answers with accompanying correctness indicators.
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