Finding the Linearization of f(x): Find the linear approximation Lo(x) of the fu

Question

Finding the Linearization of f(x): Find the linear approximation Lo(x) of the function f(x) = x/root x+1 at x = 0. Use this linearization to approximate f(0.03).

a) , calculate f(0). ANSWER:_________________________________

b) calculate f o(x) and f '(0) . ANSWER:__________________________________

c) What is Lo(x)? (Determine this by hand.)

ANSWER:_____________________________________________________________________

d) Using your answer from part (e), enter Lo(x) ?

ANSWER:____________________________________________________________

e) Plot f(x) and L(x) on the same set of axes with the x-axis varying from ?10..10 and y-axis varying from ?5..5.

Study the plot that you created.

Does Lo(x) lie ABOVE or BELOW f(x)? ANSWER:_________________________________________________

Does Lo(x) UNDER estimate or OVER estimate f(x) near x = 0? ANSWER:_____________________

f) calculate the value of Lo(x) at x = 0.03. (This is the approximate value of f(0.03).)

ANSWER:_________________________________________________________

g) calculate the actual value of f(0.03).

ANSWER:___________________________________________________________________

h) calculate the error between the approximate and the actual value.

ANSWER:_____________________________________________________________________

i) Zoom in on the plot of f(x) and L(x) by changing the x-axis to vary from 0.02..0.04 and y-axis varying from 0..0.04. Study the plot that you created. You have been estimating the value of f(x) at x = 0.03. By hand, draw a vertical line through x = 0.03 on the last plot you created.

The error in using the linear approximation rather than the actual function is represented by the distance betweenL(x) and f(x) along the line through x = 0.03. Circle this error and label it on your graph.

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