This is a Test of Mathematics Solution Subjective 90 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta
:
Draw the region of points 
in the plane, which satisfy 
.
region will bounded by lines 
, 
, 
& 
. Why is that?
First note that ( |x| \le 1 ) implies:
Similarly, if we demand ( |y| \le 1 ) (the double shaded zone).
Now if we want ( |y| \le |x| ) . This can be achieved by
when x and y are both positive (in the first quadrant); that is the region below the line x = y
when x is negative and y positive (in the second quadrant); hence the region below the line y = -x
when (x, y) is in the third quadrant.
when (x, y) is in fourth quadrant.Therefore the final region is the following shaded region:
This is a Test of Mathematics Solution Subjective 90 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta
:
Draw the region of points in the plane, which satisfy .
region will bounded by lines , , & . Why is that?
First note that ( |x| \le 1 ) implies:
Similarly, if we demand ( |y| \le 1 ) (the double shaded zone).
Now if we want ( |y| \le |x| ) . This can be achieved by
when x and y are both positive (in the first quadrant); that is the region below the line x = y when x is negative and y positive (in the second quadrant); hence the region below the line y = -x when (x, y) is in the third quadrant. when (x, y) is in fourth quadrant.Therefore the final region is the following shaded region:
