Verify the formulas in Problem 21 to 27 by contour integration or as indicated. Assume f a > 0 , m > 0. P V ∫ 0 ∞ cos m x d x x 2 − a 2 = − π 2 a sin m a
Verify the formulas in Problem 21 to 27 by contour integration or as indicated. Assume f a > 0 , m > 0. P V ∫ 0 ∞ cos m x d x x 2 − a 2 = − π 2 a sin m a
Verify the formulas in Problem 21 to 27 by contour integration or as indicated. Assume
f
a
>
0
,
m
>
0.
P
V
∫
0
∞
cos
m
x
d
x
x
2
−
a
2
=
−
π
2
a
sin
m
a
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
H.W// Solve the following D. E.:
1. y-y-3y = sin 2x
Solve the following:
a. If z = sin(5x + 3y) Find and
dx
dz
ду
b. If z=(3x+2y) (4x-5y) Find Oz
dz
and
8x by
c. A cylinder has dimensions r=5 cm, h=12 cm. Find the approximate increase in
volume when r increases by 0.2 cm and h decreases by 0.3 cm.
d. The radius of a cylinder increases at the rate of 0.2 cm/s while the height
decreases at the rate of 0.4 cm/s. Find the rate at which the volume is changing
at the instant when r = 8 cm and h = 12 cm.
e. If z=sin(x + y); x = u² + v²; y = 2uv Find
dz
and
อน
av
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