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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Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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How do I use logarithmic differentiation to solve?
![The mathematical expression given is:
\[ y = \frac{\sqrt[4]{x^2 - 2}}{x + 4} \]
This equation represents a function \( y \) in terms of the variable \( x \). The numerator of the fraction is the fourth root of the expression \( x^2 - 2 \). The denominator is a linear expression in terms of \( x \), specifically \( x + 4 \).
Understanding and analyzing such functions involves exploring their domain, range, and behavior. The presence of the fourth root places restrictions on the values \( x \) can take, as the expression under the root must be non-negative for real-number results. Additionally, the denominator must not be zero to avoid undefined values for the function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F668826ef-a7b0-4206-bae0-a08cac22bcd4%2Ffb49c3db-b416-4aa7-a5c1-a66dbdd12899%2F2z0m2v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The mathematical expression given is:
\[ y = \frac{\sqrt[4]{x^2 - 2}}{x + 4} \]
This equation represents a function \( y \) in terms of the variable \( x \). The numerator of the fraction is the fourth root of the expression \( x^2 - 2 \). The denominator is a linear expression in terms of \( x \), specifically \( x + 4 \).
Understanding and analyzing such functions involves exploring their domain, range, and behavior. The presence of the fourth root places restrictions on the values \( x \) can take, as the expression under the root must be non-negative for real-number results. Additionally, the denominator must not be zero to avoid undefined values for the function.
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