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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
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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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.
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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