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Stewart_Calc_7ET ch04sec08
MULTIPLE CHOICE
1. Estimate the value of by using three iterations of Newton’s method to solve the
equation with initial estimate Round your final estimate to four decimal
places.
a.
1.71
b.
1.6535
c.
2.2361
d.
2.2662
2. Estimate the value of by using three iterations of Newton’s method to solve the
equation with initial estimate Round your final estimate to four decimal
places.
a.
3.3166
b.
2.253
c.
3.2605
d.
2.224
3. Use Newton’s method to obtain an approximation to the root of to within
0.00001.
a.
0.20844
b.
0.2443
c.
0.22413
d.
0.2712
NUMERIC RESPONSE
1. Use Newton's method with the specified initial approximation to find , the third
approximation to the root of the given equation. (Give your answer to four decimal places.)
2. Suppose the line is tangent to the curve when . If Newton's
method is used to locate a root of the equation and the initial approximation is
, find the second approximation .
3. Use Newton's method to approximate the indicated root of in the interval
, correct to six decimal places.
Use as the initial approximation.
SHORT ANSWER
1. Use Newton’s method to find the zero of to within 0.00001 by solving
the equation using
1 2–1–2 x
1
2
3
4
–1
–2
–3
–4
y
2. Use Newton’s method to find the point of intersection of the graphs of and
to within 0.00001 by solving the equation using
3. Use Newton’s method to approximate the zero of between and
using . Continue until two successive approximations differ by less than
0.00001.
4. Approximate the zero of in to within 0.00001.
5. Use Newton’s method to solve the equation to within
0.00001.
1 2–1–2 x
1
2
3
–1
–2
–3
y
