Let
a) Find the linearization
b) Use the linearization to approximate
c) Find
d) What is the difference between the approximation and the actual value of
a) The linear approximation is
b) Using the linearization,
(Type an integer or a decimal.)
The difference between the approximation and the actual value is
Step 1 :The linearization of a function
Step 2 :First, we need to find the derivative of
Step 3 :Substituting
Step 4 :Substituting
Step 5 :Substituting these values into the linearization formula, we get
Step 6 :To approximate
Step 7 :Using a calculator, we find that
Step 8 :The difference between the approximation and the actual value is