Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13, Problem 32SP
To determine
To find:The given line integral.
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14. Consider the two vector-valued functions given by
1
r(t) = (t+1, cos
1+t
and
w(s) = (s, sin
(), ).
a. Determine the point of intersection of the curves generated by r(t) and
w(s). To do so, you will have to find values of a and b that result in r(a)
and w(b) being the same vector.
b. Use the value of a you determined in (a) to find a vector form of the
tangent line to r(t) at the point where t = a.
Sketch the slope field for
the points (ti, y;) where
at
and
dy
df
y-2
Z₁ = -1 +0.25 (1-1)
=
for 121,2,5,... 9
yj
Y; = 1 +0.25 (j-1)
for j=1,2,3,... 9
15. Consider the function f(x, y) = exy.
(a)
(b)
(c)
Determine the vector field F = Vf.
Evaluate fF. dr where C is the line segment from (1, 1) to (−1, −1).
C
Evaluate fF. dr where C is the unit circle determined by the vector-valued
C
function r(t) = (cos(t), sin(t)), 0 ≤ t ≤ 2π.
Chapter 13 Solutions
Calculus
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