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Consider the function \(f(x) = x^3 + 2x - 2\)

A student performs Newton's method beginning with initial guess \(x_0 = 1\):

1.  Which of the following is true?

a.  There is a mistake computing x₁

b.  The value x₁ is correct, but there is a mistake computing x₂

c.  The value x₂ is correct, but there is a mistake computing x₃

d.  The value x₃ is correct, but there is a mistake computing x₄

d.  There are no errors in this table.

2.  Use linear approximation to estimate the value of \(\sqrt 99\). I really want you to use linear approximation. If you just go ahead and put \(\sqrt 99\) into your calculator, you'll get the wrong answer.

a.  9.94975

b.  9.94987

c.  9.95000

d.  9.95023

3.  If you measure the radius of a circle to be 40 cm \(\pm\)1 cm, use differentials to estimate the value of the area of the circle.

a.  \( 1600\pi\) cm\(^2 \pm 80\pi\) cm\(^2\)

b.  \( 1600\pi\) cm\(^2 \pm 100\pi\) cm\(^2\)

c.  \( 1600\pi\) cm\(^2 \pm 120\pi\) cm\(^2\)

d.  \( 1600\pi\) cm\(^2 \pm 160\pi\) cm\(^2\)