If A is a positive real number, the terms of the sequence defined by a 1 = A 2 a n d a n = 1 2 ( a n − 1 + A a n − 1 ) f o r n ≥ 2 can be used to approximate A to any decimal place accuracy desired. In Problems 67 and 68, compute the first four terms of this sequence for the indicated value of A, and compare the fourth term with the value of A obtained from a calculator. 67. A = 2
If A is a positive real number, the terms of the sequence defined by a 1 = A 2 a n d a n = 1 2 ( a n − 1 + A a n − 1 ) f o r n ≥ 2 can be used to approximate A to any decimal place accuracy desired. In Problems 67 and 68, compute the first four terms of this sequence for the indicated value of A, and compare the fourth term with the value of A obtained from a calculator. 67. A = 2
Solution Summary: The author explains how to find the first four terms of the sequence a_1=A2and
If A is a positive real number, the terms of the sequence defined by
a
1
=
A
2
a
n
d
a
n
=
1
2
(
a
n
−
1
+
A
a
n
−
1
)
f
o
r
n
≥
2
can be used to approximate
A
to any decimal place accuracy desired. In Problems 67 and 68, compute the first four terms of this sequence for the indicated value of A, and compare the fourth term with the value of
A
obtained from a calculator.
(3) (16 points) Let D = [0, π/2] × [0, 7/6]. Define T: DCR2 R3 by
→
T(0, 4) = (2 sin cos 0, 2 sin sin 0, 2 cos x).
Let S be the surface parametrized by T.
(a) (8 points) Determine the normal, call it n(p), for the tangent plane TS at an
arbitrary point p = T(0, 4).
(b) (4 points) Show that n(p) parallel to the position vector T(0, 4) determined by
p? Do the two vectors have the same direction or opposite direction? Explain.
(c) (4 points) At which points p, if any, is TS parallel to the xy-plane?
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D2L HW4- AMAT100-Precal
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Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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