Consider the function f defined by f(x) its domain. a) First compute_lim f(x). Answer: x→∞ = and Q(x)? FORMATTING: 6+5e-3x 1-16e-3x b) Next we want to compute the limit in the opposite direction. As a goes to -∞, we get an indeterminate form of the type O 100 00⁰ 00x∞ 0/0 ○ ∞0/00 O∞-∞ Our goal in this question is to understand its behaviour as a goes to too, as well as near gaps in c) To be able to compute lim f(x), you have to rewrite f(x) as a fraction f(x) = x418 d) Using your answer in (c), compute lim f(x). Answer: x 8 Finally, we analyse f(x) near gaps in its domain. e) Find the point(s) a= a where f(a) is undefined. • Write your answer in the form [P(x), Q(x)], including the square brackets and comma. • Simplify so there are no fractional expressions in the numerator P(x) or denominator Q(x). • Strict calculator notation is required in your answer, meaning for multiplication (e.g. 3x is written 3*x, and e3x is written e^(3*x)). Answer: [P(x), Q(x)] = FORMATTING: List these points. If there are two or more such points, you must separate them by semi-colons (;). Since we are asking for exact values, your answers may involve the logarithm function In(). Answer: P(x) Q(x) f) For each of the values of \)a\) that you have found in (e), find the left-hand and right-hand limits of f as a approaches a. Then answer the questions below. For which point(s) a do we have lim f(x) = +∞o ? Answer: x→a that is no longer an indeterminate form. What are P(x) FORMATTING: If there are two or more points, separate them with semi-colons (). Since we are asking for exact values, your answers may involve the logarithmic function In()). You must use the notation of scientific calculators So 2x is written 2 * x, and so on. If there aren't any points, write empty. For which point(s) a do we have lim f(x) = -∞o ? Answer: x→a For which point(s) a do we have lim f(x) = +∞o ? Answer: x+a+ For which point(s) a do we have lim f(x) = -∞o ? Answer: x→a+ P a P ap
Consider the function f defined by f(x) its domain. a) First compute_lim f(x). Answer: x→∞ = and Q(x)? FORMATTING: 6+5e-3x 1-16e-3x b) Next we want to compute the limit in the opposite direction. As a goes to -∞, we get an indeterminate form of the type O 100 00⁰ 00x∞ 0/0 ○ ∞0/00 O∞-∞ Our goal in this question is to understand its behaviour as a goes to too, as well as near gaps in c) To be able to compute lim f(x), you have to rewrite f(x) as a fraction f(x) = x418 d) Using your answer in (c), compute lim f(x). Answer: x 8 Finally, we analyse f(x) near gaps in its domain. e) Find the point(s) a= a where f(a) is undefined. • Write your answer in the form [P(x), Q(x)], including the square brackets and comma. • Simplify so there are no fractional expressions in the numerator P(x) or denominator Q(x). • Strict calculator notation is required in your answer, meaning for multiplication (e.g. 3x is written 3*x, and e3x is written e^(3*x)). Answer: [P(x), Q(x)] = FORMATTING: List these points. If there are two or more such points, you must separate them by semi-colons (;). Since we are asking for exact values, your answers may involve the logarithm function In(). Answer: P(x) Q(x) f) For each of the values of \)a\) that you have found in (e), find the left-hand and right-hand limits of f as a approaches a. Then answer the questions below. For which point(s) a do we have lim f(x) = +∞o ? Answer: x→a that is no longer an indeterminate form. What are P(x) FORMATTING: If there are two or more points, separate them with semi-colons (). Since we are asking for exact values, your answers may involve the logarithmic function In()). You must use the notation of scientific calculators So 2x is written 2 * x, and so on. If there aren't any points, write empty. For which point(s) a do we have lim f(x) = -∞o ? Answer: x→a For which point(s) a do we have lim f(x) = +∞o ? Answer: x+a+ For which point(s) a do we have lim f(x) = -∞o ? Answer: x→a+ P a P ap
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Fast pls solve this question correctly in 5 min pls I will give u like for sure
Mnty
![Consider the function f defined by f(x)
its domain.
a) First compute_lim f(x). Answer:
x→∞
6+5e-3x
1-16e-3x
b) Next we want to compute the limit in the opposite direction. As a goes to -∞o, we get an indeterminate form of the type
0 100 00⁰ 00×∞ O 0/0 O ∞0/00 O ∞-∞
Our goal in this question is to understand its behaviour as a goes to too, as well as near gaps in
c) To be able to compute lim f(x), you have to rewrite f(x) as a fraction f(x) =
and Q(x)?
x →→∞
FORMATTING:
d) Using your answer in (c), compute lim f(x). Answer:
x→ ∞
Finally, we analyse f(x) near gaps in its domain.
e) Find the point(s) x = a where f(a) is undefined.
• Write your answer in the form [P(x), Q(x)], including the square brackets and comma.
• Simplify so there are no fractional expressions in the numerator P(x) or denominator Q(x).
• Strict calculator notation is required in your answer, meaning for multiplication (e.g. 3x is written 3*x, and e³ª is written e^(3*x)).
Answer: [P(x), Q(x)] =
i p
For which point(s) a do we have lim
x→a
P(x)
Q(x)
FORMATTING: List these points. If there are two or more such points, you must separate them by semi-colons (). Since we are asking for exact values, your
answers may involve the logarithm function In().
Answer:
that is no longer an indeterminate form. What are P(x)
f) For each of the values of \)a\) that you have found in (e), find the left-hand and right-hand limits of f as approaches a. Then answer the questions
below.
FORMATTING: If there are two or more points, separate them with semi-colons (;). Since we are asking for exact values, your answers may involve the
logarithmic function In()). You must use the notation of scientific calculators So 2x is written 2 * x, and so on. If there aren't any points, write empty.
For which point(s) a do we have lim f(x) = +∞ ? Answer:
x→a
f(x) = -∞ ? Answer:
For which point(s) a do we have lim f(x) = +∞o ? Answer:
x+a+
For which point(s) a do we have lim f(x) = -∞ ? Answer:
+
x→a
la P
P
GP](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba6de5e3-51c1-4a9f-86c0-e5ac1d8a9ad1%2F6c4575b1-1f55-4bec-8648-b008ff7bccbc%2F1n7lhx4o_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the function f defined by f(x)
its domain.
a) First compute_lim f(x). Answer:
x→∞
6+5e-3x
1-16e-3x
b) Next we want to compute the limit in the opposite direction. As a goes to -∞o, we get an indeterminate form of the type
0 100 00⁰ 00×∞ O 0/0 O ∞0/00 O ∞-∞
Our goal in this question is to understand its behaviour as a goes to too, as well as near gaps in
c) To be able to compute lim f(x), you have to rewrite f(x) as a fraction f(x) =
and Q(x)?
x →→∞
FORMATTING:
d) Using your answer in (c), compute lim f(x). Answer:
x→ ∞
Finally, we analyse f(x) near gaps in its domain.
e) Find the point(s) x = a where f(a) is undefined.
• Write your answer in the form [P(x), Q(x)], including the square brackets and comma.
• Simplify so there are no fractional expressions in the numerator P(x) or denominator Q(x).
• Strict calculator notation is required in your answer, meaning for multiplication (e.g. 3x is written 3*x, and e³ª is written e^(3*x)).
Answer: [P(x), Q(x)] =
i p
For which point(s) a do we have lim
x→a
P(x)
Q(x)
FORMATTING: List these points. If there are two or more such points, you must separate them by semi-colons (). Since we are asking for exact values, your
answers may involve the logarithm function In().
Answer:
that is no longer an indeterminate form. What are P(x)
f) For each of the values of \)a\) that you have found in (e), find the left-hand and right-hand limits of f as approaches a. Then answer the questions
below.
FORMATTING: If there are two or more points, separate them with semi-colons (;). Since we are asking for exact values, your answers may involve the
logarithmic function In()). You must use the notation of scientific calculators So 2x is written 2 * x, and so on. If there aren't any points, write empty.
For which point(s) a do we have lim f(x) = +∞ ? Answer:
x→a
f(x) = -∞ ? Answer:
For which point(s) a do we have lim f(x) = +∞o ? Answer:
x+a+
For which point(s) a do we have lim f(x) = -∞ ? Answer:
+
x→a
la P
P
GP
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