e. lim 5r3 +8r _4 10x³ +3x+1 g. lim x² sin x→0+ ( (Hint: Use the Squeeze Thm) f. lim ∞0-7x 16x³ +7x² 12x³ +√16x¹⁰ +1
e. lim 5r3 +8r _4 10x³ +3x+1 g. lim x² sin x→0+ ( (Hint: Use the Squeeze Thm) f. lim ∞0-7x 16x³ +7x² 12x³ +√16x¹⁰ +1
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
Find the indicated limits, if they exist (leave answers exact). Be sure to show all work!
![Sure! Here is the transcription for an educational website:
---
### Calculus Limits Problems
**Problem e.**
Evaluate the limit:
\[
\lim_{x \to \infty} \frac{5x^3 + 8x^2 - 4}{10x^3 + 3x + 1}
\]
**Problem f.**
Evaluate the limit:
\[
\lim_{x \to -\infty} \frac{16x^5 + 7x^2}{12x^5 + \sqrt{16x^{10}} + 1}
\]
**Problem g.**
Evaluate the limit:
\[
\lim_{x \to 0^+} x^2 \sin\left(\frac{1}{x}\right)
\]
(*Hint: Use the Squeeze Theorem*)
---
These problems focus on evaluating limits of rational functions and trigonometric expressions. Problem g hints at using the Squeeze Theorem to find the limit as \( x \) approaches 0 from the positive side.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc84d0291-1107-4711-af5a-30afb213fbbf%2F9d7666b7-c2ae-4958-a38d-5afcc7c562c8%2F92lz9ie_processed.png&w=3840&q=75)
Transcribed Image Text:Sure! Here is the transcription for an educational website:
---
### Calculus Limits Problems
**Problem e.**
Evaluate the limit:
\[
\lim_{x \to \infty} \frac{5x^3 + 8x^2 - 4}{10x^3 + 3x + 1}
\]
**Problem f.**
Evaluate the limit:
\[
\lim_{x \to -\infty} \frac{16x^5 + 7x^2}{12x^5 + \sqrt{16x^{10}} + 1}
\]
**Problem g.**
Evaluate the limit:
\[
\lim_{x \to 0^+} x^2 \sin\left(\frac{1}{x}\right)
\]
(*Hint: Use the Squeeze Theorem*)
---
These problems focus on evaluating limits of rational functions and trigonometric expressions. Problem g hints at using the Squeeze Theorem to find the limit as \( x \) approaches 0 from the positive side.
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