Two parameterizations Verify that ∮ C ( x − 2 y + 3 z ) d s has the same value when C is given by r ( t ) = 〈2 cos t , 2 sin t , 0〉, for 0 ≤ t ≤ 2 π , and by r ( t ) = 〈2 cos t 2 , 2 sin t 2 , 0〉, for 0 ≤ t ≤ 2 π .
Two parameterizations Verify that ∮ C ( x − 2 y + 3 z ) d s has the same value when C is given by r ( t ) = 〈2 cos t , 2 sin t , 0〉, for 0 ≤ t ≤ 2 π , and by r ( t ) = 〈2 cos t 2 , 2 sin t 2 , 0〉, for 0 ≤ t ≤ 2 π .
Two parameterizations Verify that
∮
C
(
x
−
2
y
+
3
z
)
d
s
has the same value when C is given by r(t) = 〈2 cos t, 2 sin t, 0〉, for 0 ≤ t ≤ 2π, and by r(t) = 〈2 cos t2, 2 sin t2, 0〉, for
0
≤
t
≤
2
π
.
The velocity of a particle moves along the x-axis and is given by the equation ds/dt = 40 - 3t^2 m/s. Calculate the acceleration at time t=2 s and t=4 s. Calculate also the total displacement at the given interval. Assume at t=0 s=5m.Write the solution using pen and draw the graph if needed.
The velocity of a particle moves along the x-axis and is given by the equation ds/dt = 40 - 3t^2 m/s. Calculate the acceleration at time t=2 s and t=4 s. Calculate also the total displacement at the given interval. Assume at t=0 s=5m.Write the solution using pen and draw the graph if needed.
4. Use method of separation of variable to solve the following wave equation
მłu
J²u
subject to
u(0,t) =0, for t> 0,
u(л,t) = 0, for t> 0,
=
t> 0,
at²
ax²'
u(x, 0) = 0,
0.01 x,
ut(x, 0) =
Π
0.01 (π-x),
0
Chapter 17 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
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