Question
For each function below find the best linear approximation (linearization) at the given value.
f(x) = x^-1 at x = 2
y = 1/2
f ' (x) = -1x^-2 at x = 2 : -1/4
y - 1/2 = -1/4 (x-2)
y - 1/2 = -1/4x + 1/2
y = -1/4x + 1
Use the appropriate linearization above to find approximate values for the following, then use your calculator to find the exact values and compute the error in your approximation.
1/2.04
The error is 0.0001961 but I'm not sure how to get it. Can someone please help me?
f(x) = x^-1 at x = 2
y = 1/2
f ' (x) = -1x^-2 at x = 2 : -1/4
y - 1/2 = -1/4 (x-2)
y - 1/2 = -1/4x + 1/2
y = -1/4x + 1
Use the appropriate linearization above to find approximate values for the following, then use your calculator to find the exact values and compute the error in your approximation.
1/2.04
The error is 0.0001961 but I'm not sure how to get it. Can someone please help me?
Answers
Steve
well, the error is the approximate value minus the real value.