Let P(x) = 2x² +5x+5. Give a step-by-ste- & proof to show that P(x) is continuous at x = -2. (Hint: rewrite the definition of lim-2 P(x) = P(-2), substituting the actual values for generic terms. Set a temporary bound bon |z − (−2)| = |x + 2), and find a bound M on Q(x)\, where |P(x) – P(−2)| = |Q(x)(x + 2)| = |Q(x)||x + 2| ≤ M|x + 2| < €. Then & min(b, c/M} will work.)
Let P(x) = 2x² +5x+5. Give a step-by-ste- & proof to show that P(x) is continuous at x = -2. (Hint: rewrite the definition of lim-2 P(x) = P(-2), substituting the actual values for generic terms. Set a temporary bound bon |z − (−2)| = |x + 2), and find a bound M on Q(x)\, where |P(x) – P(−2)| = |Q(x)(x + 2)| = |Q(x)||x + 2| ≤ M|x + 2| < €. Then & min(b, c/M} will work.)
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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Wksp 4 Q6
PLEASE PLEASE include labeled definition(AS IT APPLIES TO THE QUESTION), scratchwork, and proof
![Let P(x) = 2x² +5x+5. Give a step-by-ste- & proof to show that P(x) is continuous
at x = -2.
(Hint: rewrite the definition of lim-2 P(x) = P(-2), substituting the actual values
for generic terms. Set a temporary bound bon |z − (−2)| = |x + 2), and find a bound
M on Q(x)\, where |P(z) – P(-2)| = |Q(1)(x + 2)| = |Q(1)||x + 2] ≤ M\x + 2| < €.
Then 6 min (b, e/M} will work.)
Definition.
Scratch work.
Proof.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6039e52-60b3-4ae1-b575-68d9236f4955%2Fd77e7da1-5f62-4993-94e0-b06a9db489a8%2Fc79gy9g_processed.png&w=3840&q=75)
Transcribed Image Text:Let P(x) = 2x² +5x+5. Give a step-by-ste- & proof to show that P(x) is continuous
at x = -2.
(Hint: rewrite the definition of lim-2 P(x) = P(-2), substituting the actual values
for generic terms. Set a temporary bound bon |z − (−2)| = |x + 2), and find a bound
M on Q(x)\, where |P(z) – P(-2)| = |Q(1)(x + 2)| = |Q(1)||x + 2] ≤ M\x + 2| < €.
Then 6 min (b, e/M} will work.)
Definition.
Scratch work.
Proof.
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