Concept explainers
a.
To calculate the coefficients
a.
Answer to Problem 66E
Explanation of Solution
Given information:
Quadratic approximation to
With the properties
Calculation :
Write the function and get the values at
Therefore,
b.
To find the quadratic approximation to
b.
Answer to Problem 66E
The quadratic approximation is
Explanation of Solution
Given information:
The given statement is that find the quadratic approximation to
Calculation :
Substitute the values in quadratic approximation equation
Therefore,
The quadratic approximation is
c.
To graph:
c.
Explanation of Solution
Given information:
ZOOM IN on the two graphs at point
Graph:
The graph of
The image of ZOOM IN at point
Interpretation:
At the point
d.
To find the quadratic approximation to
d.
Answer to Problem 66E
The quadratic approximation is
The function and its approximation behave similar around
Explanation of Solution
Given information:
The given statement is that find the quadratic approximation to
Calculation :
Substitute the values in quadratic approximation equation
Therefore,
The quadratic approximation is
The graph of g and its quadratic approximation together.
The function and its approximation behave similar around
e.
To find the quadratic approximation to
e.
Answer to Problem 66E
The quadratic approximation is
The function and its approximation behave similar around
Explanation of Solution
Given information:
The given statement is that find the quadratic approximation to
Calculation :
Substitute the values in quadratic approximation equation
Therefore,
The quadratic approximation is
The graph of h and its quadratic approximation together.
The function and its approximation behave similar around
f.
To write the linearization of f , g , and h at the respective points.
f.
Answer to Problem 66E
Linearization of f , g , and h are
Explanation of Solution
Given information:
Functions are given in parts (b), (d), and (e)
Formula used:
Linearization.
Calculation :
For f
Linearization.
For g
Linearization.
For h
Linearization.
Therefore,
Linearization of f , g , and h are
Chapter 5 Solutions
Calculus: Graphical, Numerical, Algebraic
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