A)Calculate f(0)? B)Calculate f\'(x) and f \'(0) ? C) What is L0(x)? (Determine

ID: 3288982 • Letter: A

Question

A)Calculate f(0)?

B)Calculate f'(x) and f '(0) ?

C) What is L0(x)? (Determine this by hand.)

D) 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.

Does L0(x) lie ABOVE or BELOW f(x)? ANSWER:

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

E)Calculate the value of L0(x) at x = 0.03. (This is the approximate value of f(0.03).)

F)Calculate the actual value of f(0.03).

G) Calculate the error between the approximate and the actual value.

H)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. 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.

L(x) and f(x) along the line through x = 0.03. Circle this error and label it on your graph.

1)0

2)(sqrt(x+1)+(x(x+1)^-1/2)/2)/x+1) and 1

3)lox= f(x)+f'(x)(x-a) at x=a

lox lie above f(x)

4)over estimate at x=0

5)lox at 0.03 will be 0.03 as at x=0 lox=x

6)actual volue of f(0.03)=0.2955

7)error is 0.0045

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