Topic: Graphing on Intervals (-8, 8) Instructions: 1.) Using any graphical app, construct three different graphs which lie on interval (-8, 8). (Attach photo of graph) 2.) Choose three different intervals. 3.) Prove that these intervals are continuous. See picture (This is an example of this activity). This serves as a guide :) Thank u!
Topic: Graphing on Intervals (-8, 8) Instructions: 1.) Using any graphical app, construct three different graphs which lie on interval (-8, 8). (Attach photo of graph) 2.) Choose three different intervals. 3.) Prove that these intervals are continuous. See picture (This is an example of this activity). This serves as a guide :) Thank u!
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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Topic: Graphing on Intervals (-8, 8)
Instructions:
1.) Using any graphical app, construct three different graphs which lie on interval (-8, 8). (Attach photo of graph)
2.) Choose three different intervals.
3.) Prove that these intervals are continuous.
See picture (This is an example of this activity). This serves as a guide :) Thank u!
![Question (see above)
EXAMPLE ONLY:
3. x? + 5x – 5 on [-6, 2]
Proving that the function f(x) = x? + 5x – 5 is continuous based on the interval [-6,2]
Step 1:
f(x) = x? + 5x - 5
-5.92 + 5(-5.9) – 5
-5.52 + + 5(-5.5) – 5
-52 + 5(-5) – 5
X-values
y-values
-5.9
0.31
-5.5
- 2.25
-5
-5
It is continuous because, all domains (x-values) in between (-6, 2) have its own defined y-value.
Step 2: Determine if f(x) = x² + 5x – 5 is oontinuous at the left endpoint [-6]
a. Evaluate the function
f(x) = x? + 5x – 5 x = -6
f(-8) = (-6)² + 5(-6) – 5 = 1
b. Find the lim x? + 5x – 5
5
-10
10
lim x? +
lim 5x -
lim 5 =(-6)2 + 5(-6) – 5 = 1
c. If f(a)
lim f(x)
1
1
Step 3: Determine if f(x) = x² + 5x – 5 is continuous at the right endpoint [2]
a. Evaluate the function
f(x) = x? + 5x – 5
x = 2
f(-8) = (2)2 + 5(2) – 5 = 9
b. Find the lim x? + 5x – 7
lim x? +
lim 5x - lim 5 =(8)? + 5(8) – 7 = 9
* + 2
c. If f(a)
lim f(x)
9
Conclusion: Since all of the three conditions were satisfied, therefore proving that the function f(x) =
x2 + 5x – 5 is continuous based on the interval [-6,2]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1f2c132-1439-42c7-b4cb-11c574c8a62f%2F4ded6b09-0e9d-4a70-a423-a2defb19fde8%2Fwt5gtu7_processed.png&w=3840&q=75)
Transcribed Image Text:Question (see above)
EXAMPLE ONLY:
3. x? + 5x – 5 on [-6, 2]
Proving that the function f(x) = x? + 5x – 5 is continuous based on the interval [-6,2]
Step 1:
f(x) = x? + 5x - 5
-5.92 + 5(-5.9) – 5
-5.52 + + 5(-5.5) – 5
-52 + 5(-5) – 5
X-values
y-values
-5.9
0.31
-5.5
- 2.25
-5
-5
It is continuous because, all domains (x-values) in between (-6, 2) have its own defined y-value.
Step 2: Determine if f(x) = x² + 5x – 5 is oontinuous at the left endpoint [-6]
a. Evaluate the function
f(x) = x? + 5x – 5 x = -6
f(-8) = (-6)² + 5(-6) – 5 = 1
b. Find the lim x? + 5x – 5
5
-10
10
lim x? +
lim 5x -
lim 5 =(-6)2 + 5(-6) – 5 = 1
c. If f(a)
lim f(x)
1
1
Step 3: Determine if f(x) = x² + 5x – 5 is continuous at the right endpoint [2]
a. Evaluate the function
f(x) = x? + 5x – 5
x = 2
f(-8) = (2)2 + 5(2) – 5 = 9
b. Find the lim x? + 5x – 7
lim x? +
lim 5x - lim 5 =(8)? + 5(8) – 7 = 9
* + 2
c. If f(a)
lim f(x)
9
Conclusion: Since all of the three conditions were satisfied, therefore proving that the function f(x) =
x2 + 5x – 5 is continuous based on the interval [-6,2]
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