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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![**Find the limit.**
\[ \lim_{{h \to 0}} \frac{{8}}{{(t+h)^4}} - \frac{{8}}{{t^4}} \]
The task is to find the limit of the function as \( h \) approaches 0.
In this problem, the expression involves a difference of two fractions inside the limit. The numerator of each fraction includes the constant 8 and the denominator includes the variables \( (t+h)^4 \) and \( t^4 \). The entire expression is then divided by \( h \).
Understanding this limit is essential for calculus students, as it provides insights into differentiating functions involving exponents and deeply explores the limits of functions. This type of problem typically requires techniques such as algebraic manipulation or the application of L'Hopital's Rule to solve.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b8b635d-64c7-420e-93b9-2c6bfd1ef1b9%2F27285de7-18ac-407b-9138-969e8239030f%2Fqgexxrr_reoriented.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the limit.**
\[ \lim_{{h \to 0}} \frac{{8}}{{(t+h)^4}} - \frac{{8}}{{t^4}} \]
The task is to find the limit of the function as \( h \) approaches 0.
In this problem, the expression involves a difference of two fractions inside the limit. The numerator of each fraction includes the constant 8 and the denominator includes the variables \( (t+h)^4 \) and \( t^4 \). The entire expression is then divided by \( h \).
Understanding this limit is essential for calculus students, as it provides insights into differentiating functions involving exponents and deeply explores the limits of functions. This type of problem typically requires techniques such as algebraic manipulation or the application of L'Hopital's Rule to solve.
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