uments/MAZ30%20Multi/Further20Mathematics20for20Economic20Analysis%20by20K OSydsaeter Peter%20Hammond Atle20Seierstad Arne20Strom20z-lib.orgi.pdf Knut Sydsaeter,Peter Hammond Atle Selerstad,Ar. 33 / 310 2. Determine which of the following sets are convex by drawing each in the xy-plane. (a) {(x, y) : x + y? < 2} (b) {(x, y) : x 2 0, y 2 0} (c) {(x, y) : x? + y² > 8} (d) {(x, y) : x 2 0, y 2 0, xy 1} (f) {(x, y) : + vJ S 2} (e) {(x, y) : xy < 1} 3. Let S be the set of all points (x1, ..., xn) in R" that satisfy all the m inequalities ... I95 "x"lp +· + txllp + lxllp ... ... + amn Xn s bm ... and moreover are such that x, 2 0, . , xn 0. Show that S is a convex set. 1:15 AM

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Chapter2: Second-order Linear Odes
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SULVENS INSTITUTE
uments/MA230%620Multi/Further%20Mathematics%20for%20Economic%20Analysis%20by%20Knut%20Sydsaeter,Peter%20Hammond, Atle%20Seierstad Arne%20Strom%20(z-lib.org).pdf
Knut Sydsaeter,Peter Hammond,Atle Selerstad,Ar.
33 / 310
2. Determine which of the following sets are convex by drawing each in the xy-plane.
(a) {(x,y):x² + y? < 2}
(c) {(x, y): x² + y?
(b) {(x, y) : x > 0, y > 0}
(d) {(x, y) : x > 0, y > 0, xy > 1}
{8 <
(e) {(x, y): xy < 1}
(f) {(x, y) : Jx + vý s 2}
3. Let S be the set of all points (x1,...
, xn) in R" that satisfy all the m inequalities
A2¡X1 + a22x2 + · · ·+ az Xn < bz
Am1X1 + am2x2 + · + amn Xn < bm
and moreover are such that x, 2 0, . .., Xn 0. Show that S is a convex set.
1:15 AM
3/7/2021
1ock
6.
Transcribed Image Text:care SULVENS INSTITUTE uments/MA230%620Multi/Further%20Mathematics%20for%20Economic%20Analysis%20by%20Knut%20Sydsaeter,Peter%20Hammond, Atle%20Seierstad Arne%20Strom%20(z-lib.org).pdf Knut Sydsaeter,Peter Hammond,Atle Selerstad,Ar. 33 / 310 2. Determine which of the following sets are convex by drawing each in the xy-plane. (a) {(x,y):x² + y? < 2} (c) {(x, y): x² + y? (b) {(x, y) : x > 0, y > 0} (d) {(x, y) : x > 0, y > 0, xy > 1} {8 < (e) {(x, y): xy < 1} (f) {(x, y) : Jx + vý s 2} 3. Let S be the set of all points (x1,... , xn) in R" that satisfy all the m inequalities A2¡X1 + a22x2 + · · ·+ az Xn < bz Am1X1 + am2x2 + · + amn Xn < bm and moreover are such that x, 2 0, . .., Xn 0. Show that S is a convex set. 1:15 AM 3/7/2021 1ock 6.
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