dy = f'(x). use your eguation to estimate the express the relationship etheen a small change in X d coreponding chame i in form t + (x)x. use yaur. eguaticn to estimate the regnested value of fcX). メレX fx) = Sin (Sx²) baseline X estimate f(80) tuse radian + xkX X- 79.9967 13
dy = f'(x). use your eguation to estimate the express the relationship etheen a small change in X d coreponding chame i in form t + (x)x. use yaur. eguaticn to estimate the regnested value of fcX). メレX fx) = Sin (Sx²) baseline X estimate f(80) tuse radian + xkX X- 79.9967 13
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
![**Exploring the Relationship Between Small Changes in Variables**
In this exercise, we will explore the mathematical relationship between a small change in \( x \) and the corresponding change in \( y \). The expression to be used is \( dy = f'(x)dx \). This equation will help us estimate the requested value of \( f(x) \).
### Given Function
The function is defined as:
\[
f(x) = \sin(5x^2)
\]
### Estimation Objective
Our goal is to estimate the function value \( f(80) \).
**Baseline Value:**
\[
x = 79.9967
\]
**Note:** Use radian mode for calculations.
This exercise helps in understanding how differential calculus can be applied to make estimations of function values using small changes in the independent variable \( x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3341284f-d761-40a1-94fb-8b0932aec828%2Fcbd22f1c-4274-4f2d-845d-c4373725bcc8%2F0hnfy6o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exploring the Relationship Between Small Changes in Variables**
In this exercise, we will explore the mathematical relationship between a small change in \( x \) and the corresponding change in \( y \). The expression to be used is \( dy = f'(x)dx \). This equation will help us estimate the requested value of \( f(x) \).
### Given Function
The function is defined as:
\[
f(x) = \sin(5x^2)
\]
### Estimation Objective
Our goal is to estimate the function value \( f(80) \).
**Baseline Value:**
\[
x = 79.9967
\]
**Note:** Use radian mode for calculations.
This exercise helps in understanding how differential calculus can be applied to make estimations of function values using small changes in the independent variable \( x \).
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