Solution Found!
In Exercises 39–44, each function ƒ(x) changes value when
Chapter 3, Problem 39E(choose chapter or problem)
In Exercises 39–44, each function \(f(x)\) changes value when x changes from \(x_{0} \text { to } x_{0}+d x\). Find
a. the change \(\Delta f=f\left(x_{0}+d x\right)-f\left(x_{0}\right)\);
b. the value of the estimate \(d f=f^{\prime}\left(x_{0}\right) d x\); and
c. the approximation error \(|\Delta f-d f|\).
\(f(x)=x^{2}+2 x, \quad x_{0}=1, \quad d x=0.1\)
Equation Transcription:
Text Transcription:
f(x)
x_0 to x_0 + dx
delta f = f(x_0 +dx) - f(x_0);
df - f prime (x_0 ) dx
| delta f - df |
f(x)=x^2 +2x, x_0 =1 , dx=0.1
Questions & Answers
QUESTION:
In Exercises 39–44, each function \(f(x)\) changes value when x changes from \(x_{0} \text { to } x_{0}+d x\). Find
a. the change \(\Delta f=f\left(x_{0}+d x\right)-f\left(x_{0}\right)\);
b. the value of the estimate \(d f=f^{\prime}\left(x_{0}\right) d x\); and
c. the approximation error \(|\Delta f-d f|\).
\(f(x)=x^{2}+2 x, \quad x_{0}=1, \quad d x=0.1\)
Equation Transcription:
Text Transcription:
f(x)
x_0 to x_0 + dx
delta f = f(x_0 +dx) - f(x_0);
df - f prime (x_0 ) dx
| delta f - df |
f(x)=x^2 +2x, x_0 =1 , dx=0.1
ANSWER:
Solution:
Step 1 of 4:
Here, we have to find the following.
Given ,
and
.