(a) Recall that dA gives us the area of a region R in the xy-plane. Find the area of the region R = {(0,r): 0 < 0 < 0

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10th Edition
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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l.
(a) Recall that
dA gives us the area of a region R in the xy-plane. Find the area of
the region
R = {(0, r): 0 < 0 <
0 <r< 3 sec 0
6.
S 3seco}.
If necessary, round your answer to three decimal places.
Area of region R
(b) As 0 varies from
to
2'
2
the equation r = 3 sec 0 describes a line in the xy-
plane. What is the equation of the line in terms of rectangular (Cartesian) coordinates?
(Hint: Recall that x = r cos 0.)
(c) As r varies across the interval ( – 0, ), the equation 0
describes a line in
the xy-plane. What is the equation of the line in terms of rectangular (Cartesian)
coordinates? (Hint: Sketch the line and try to determine its slope.) Use the exact value of
the slope when entering in the equation.
Transcribed Image Text:l. (a) Recall that dA gives us the area of a region R in the xy-plane. Find the area of the region R = {(0, r): 0 < 0 < 0 <r< 3 sec 0 6. S 3seco}. If necessary, round your answer to three decimal places. Area of region R (b) As 0 varies from to 2' 2 the equation r = 3 sec 0 describes a line in the xy- plane. What is the equation of the line in terms of rectangular (Cartesian) coordinates? (Hint: Recall that x = r cos 0.) (c) As r varies across the interval ( – 0, ), the equation 0 describes a line in the xy-plane. What is the equation of the line in terms of rectangular (Cartesian) coordinates? (Hint: Sketch the line and try to determine its slope.) Use the exact value of the slope when entering in the equation.
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