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Explore the Back-StoryThis 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:

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