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). An ellipse circumscribes a rectangle whose sides are given by x = +2 and y = 14. If the distance between the foci is 4/6 and major axis is along y-axis, then find the equation of the ellipse. %3D
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). An ellipse circumscribes a rectangle whose sides are given by x = +2 and y = 14. If the distance between the foci is 4/6 and major axis is along y-axis, then find the equation of the ellipse. %3D
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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Question
Ques no. 4
Transcribed Image Text:1. Find the critical points, inflection points and asymptotes (if any) for the function
f(x) = Determine the region where the function increase or decrease and also
discuss it's concavity.
2. Evaluate the following limits using L'Hopital's rule:
limx-b-bb
and lim,(x-In(rs- 1010)).
xy"
3. Let f(x, y) = r+yan (x,y) # (0,0)
where n > 1.
0,
(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).
4. 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).
An ellipse circumscribes a rectangle whose sides are given by x =
the distance between the foci is 4V6 and major axis is along y-axis, then find the
equation of the ellipse.
12 and y = +4. If
= In(x² +y2 + z?), x = ue" sin u, y = ue" cos u and z = ue",
using chain rule at the point (u, v) = (-2,0).
5. If
W =
find
aw
and
du
aw
dv
6. Find the directions in which the function f(x,y,z) Inxy + In yz + In xz increase
and decrease most rapidly at the point Po(1,1,1). Then find the derivatives of the
function in those directions.
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