Answered: 3x(x - : lim Tx - 1| X1+

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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$The image contains a mathematical limit expression, which is often covered in calculus courses. Here is the transcription for educational purposes: --- **Problem 29: Evaluate the Limit** \[ \lim_{x \to 1^{+}} \frac{\sqrt{3(x-1)}}{|x-1|} \] This problem involves evaluating the limit of a function as $ x $ approaches 1 from the right ($ x \to 1^{+} $). --- In this limit problem, you are dealing with the behavior of the function as $ x $ gets arbitrarily close to 1 from the right side. This involves understanding the numerator and the absolute value function in the denominator and how they affect the evaluation near the point of interest. For $ x \to 1^{+} $, the expression inside the square root is always non-negative, and the absolute value expression in the denominator simplifies differently based on the sign of $ x-1 $.$

Transcribed Image Text:The image contains a mathematical limit expression, which is often covered in calculus courses. Here is the transcription for educational purposes: --- **Problem 29: Evaluate the Limit** \[ \lim_{x \to 1^{+}} \frac{\sqrt{3(x-1)}}{|x-1|} \] This problem involves evaluating the limit of a function as $ x $ approaches 1 from the right ($ x \to 1^{+} $). --- In this limit problem, you are dealing with the behavior of the function as $ x $ gets arbitrarily close to 1 from the right side. This involves understanding the numerator and the absolute value function in the denominator and how they affect the evaluation near the point of interest. For $ x \to 1^{+} $, the expression inside the square root is always non-negative, and the absolute value expression in the denominator simplifies differently based on the sign of $ x-1 $.

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