Problem 3. Evaluate each limit. If the limit is infinite, state whether it is -∞ or +∞. If the limit does not exist, say DNE. 2x x²-x-6 x²-4 (a) lim x-2x+2' (b) lim (c) lim (d) lim √1+t-√1-t t " x-1-x- x-3- |x - 3| t-0 1'
Problem 3. Evaluate each limit. If the limit is infinite, state whether it is -∞ or +∞. If the limit does not exist, say DNE. 2x x²-x-6 x²-4 (a) lim x-2x+2' (b) lim (c) lim (d) lim √1+t-√1-t t " x-1-x- x-3- |x - 3| t-0 1'
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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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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![**Problem 3: Evaluate Each Limit**
In this exercise, you are asked to evaluate various limits. If the limit is infinite, specify whether it is \( -\infty \) or \( +\infty \). If the limit does not exist, indicate this by writing "DNE" (Does Not Exist).
**(a)**
\[ \lim_{{x \to 2}} \frac{x^2 - 4}{x + 2} \]
**(b)**
\[ \lim_{{x \to 1^-}} \frac{2x}{x - 1} \]
**(c)**
\[ \lim_{{x \to 3}} \frac{x^2 - x - 6}{|x - 3|} \]
**(d)**
\[ \lim_{{t \to 0}} \frac{\sqrt{1 + t} - \sqrt{1 - t}}{t} \]
For each limit, apply appropriate limit laws, factorization, or other calculus techniques to determine the value, if it exists. If the limit does not converge to a finite value, make sure to indicate whether it tends to positive or negative infinity, or if it does not exist.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4526b347-f4c2-4959-b519-c79fc40f5b52%2F8d0fe906-bc5e-4f3b-aa00-d7b322cad277%2Fl4rz7py_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 3: Evaluate Each Limit**
In this exercise, you are asked to evaluate various limits. If the limit is infinite, specify whether it is \( -\infty \) or \( +\infty \). If the limit does not exist, indicate this by writing "DNE" (Does Not Exist).
**(a)**
\[ \lim_{{x \to 2}} \frac{x^2 - 4}{x + 2} \]
**(b)**
\[ \lim_{{x \to 1^-}} \frac{2x}{x - 1} \]
**(c)**
\[ \lim_{{x \to 3}} \frac{x^2 - x - 6}{|x - 3|} \]
**(d)**
\[ \lim_{{t \to 0}} \frac{\sqrt{1 + t} - \sqrt{1 - t}}{t} \]
For each limit, apply appropriate limit laws, factorization, or other calculus techniques to determine the value, if it exists. If the limit does not converge to a finite value, make sure to indicate whether it tends to positive or negative infinity, or if it does not exist.
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