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
Find F'(x)
![The image shows a mathematical expression for a function \( F(x) \) defined as an integral:
\[ F(x) = \int_{2}^{x} \frac{1}{t} \, dt \]
This indicates that \( F(x) \) is the result of integrating the function \( \frac{1}{t} \) with respect to \( t \), starting from the lower limit of 2 up to the upper limit of \( x \).
In calculus, this type of integral is known as a definite integral, which represents the accumulated area under the curve of \( \frac{1}{t} \) between the specified limits. This function is related to the natural logarithm, as the integral of \( \frac{1}{t} \) is \( \ln |t| \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e8eaad3-4d91-4777-be35-ba41f897f0fa%2Fa56e5fb5-e009-4582-8869-10ed8f2220b4%2F1dsf5uq_processed.png&w=3840&q=75)
Transcribed Image Text:The image shows a mathematical expression for a function \( F(x) \) defined as an integral:
\[ F(x) = \int_{2}^{x} \frac{1}{t} \, dt \]
This indicates that \( F(x) \) is the result of integrating the function \( \frac{1}{t} \) with respect to \( t \), starting from the lower limit of 2 up to the upper limit of \( x \).
In calculus, this type of integral is known as a definite integral, which represents the accumulated area under the curve of \( \frac{1}{t} \) between the specified limits. This function is related to the natural logarithm, as the integral of \( \frac{1}{t} \) is \( \ln |t| \).
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