3. Find the volume of the solid obtained by revolving the region bounded by the curves y = 2x2 + 1 and y = 3 - 2x2 about x-axis. Also find the length of the plane curve y = 2x2 + 1 over the interval [1, 3] %3!
3. Find the volume of the solid obtained by revolving the region bounded by the curves y = 2x2 + 1 and y = 3 - 2x2 about x-axis. Also find the length of the plane curve y = 2x2 + 1 over the interval [1, 3] %3!
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![discuss its concavity. Also, sketch the curve.
2. Evaluate the following limits using L'Hopital's rule
and lim,x- In(x5 – 1010)].
limxb
x*ーb5
3. Find the volume of the solid obtained by revolving the region bounded by the curves
y = 2x2 + 1 and y = 3 - 2x2 about x-axis. Also find the length of the plane curve
y = 2x2 + 1 over the interval [1, 3]
4. Sketch the graph of r² = 0²,0 < 0 in polar coordinates.
xyn
(x, y) + (0,0)
5. Let f(x, y) = x*+y3n!
0,
where n > 1.
(x, y) = (0,0)
Discuss the continuity of f(x,y). And show that f,(x, y) and f,(x,y) exist at all
points (x, y).
6. Find the equation of parabola which has axis parallel to y-axis and which passes
through the points (0, 2), (–1,0) and (1, 6). And plot this parabola.
An ellipse circumscribes a rectangle whose sides are given by x = +2 and y = +4. If
the distance between the foci is 4V6 and major axis is along y-axis, then find the
equation of the ellipse. Also, plot this ellipse.
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Transcribed Image Text:discuss its concavity. Also, sketch the curve.
2. Evaluate the following limits using L'Hopital's rule
and lim,x- In(x5 – 1010)].
limxb
x*ーb5
3. Find the volume of the solid obtained by revolving the region bounded by the curves
y = 2x2 + 1 and y = 3 - 2x2 about x-axis. Also find the length of the plane curve
y = 2x2 + 1 over the interval [1, 3]
4. Sketch the graph of r² = 0²,0 < 0 in polar coordinates.
xyn
(x, y) + (0,0)
5. Let f(x, y) = x*+y3n!
0,
where n > 1.
(x, y) = (0,0)
Discuss the continuity of f(x,y). And show that f,(x, y) and f,(x,y) exist at all
points (x, y).
6. Find the equation of parabola which has axis parallel to y-axis and which passes
through the points (0, 2), (–1,0) and (1, 6). And plot this parabola.
An ellipse circumscribes a rectangle whose sides are given by x = +2 and y = +4. If
the distance between the foci is 4V6 and major axis is along y-axis, then find the
equation of the ellipse. Also, plot this ellipse.
%3D
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