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x2 X tet tx et + 1 A. lim x 2 B. lim - 3-1 2 - C. lim x⇒1 x² + x 2 x² - 1 Remember that if you choose to use L'Hospital's rule, you must check all necessary assumptions and use proper notation. None of these limits require L'Hospital's rule.

x2 X tet tx et + 1 A. lim x 2 B. lim - 3-1 2 - C. lim x⇒1 x² + x 2 x² - 1 Remember that if you choose to use L'Hospital's rule, you must check all necessary assumptions and use proper notation. None of these limits require L'Hospital's rule.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
**Evaluating Limits Algebraically** For the following limits, evaluate them algebraically if they exist, showing all your work as done in lecture. If the limit does not exist, answer DNE; if it is infinity, answer ∞; if it is negative infinity, answer −∞. Leave answers in exact form (i.e., if the answer is 1/4, you may answer 1/4 or 0.25, but if the answer is 1/3, you must leave it as 1/3). Arguments that use numerical estimation or a graph will receive 0 credit. It is especially important to show all your work for these questions. **A. \(\lim_{{x \to 2}} \frac{\sqrt{x^2 - 3} - 1}{x - 2}\)** **B. \(\lim_{{t \to \infty}} \frac{te^t}{e^t + 1}\)** **C. \(\lim_{{x \to 1}} \frac{x^2 + x - 2}{x^2 - 1}\)** **Important Note:** Remember that if you choose to use L'Hospital's rule, you must check all necessary assumptions and use proper notation. None of these limits require L'Hospital's rule.
Transcribed Image Text:**Evaluating Limits Algebraically** For the following limits, evaluate them algebraically if they exist, showing all your work as done in lecture. If the limit does not exist, answer DNE; if it is infinity, answer ∞; if it is negative infinity, answer −∞. Leave answers in exact form (i.e., if the answer is 1/4, you may answer 1/4 or 0.25, but if the answer is 1/3, you must leave it as 1/3). Arguments that use numerical estimation or a graph will receive 0 credit. It is especially important to show all your work for these questions. **A. \(\lim_{{x \to 2}} \frac{\sqrt{x^2 - 3} - 1}{x - 2}\)** **B. \(\lim_{{t \to \infty}} \frac{te^t}{e^t + 1}\)** **C. \(\lim_{{x \to 1}} \frac{x^2 + x - 2}{x^2 - 1}\)** **Important Note:** Remember that if you choose to use L'Hospital's rule, you must check all necessary assumptions and use proper notation. None of these limits require L'Hospital's rule.
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