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
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Draw the region of points $ {\displaystyle{(x,y)}}$ in the plane, which satisfy $ {\displaystyle{|y| {\le} |x| {\le} 1}}$.
$ {\displaystyle{|y| {\le} |x| {\le} 1}}$ region will bounded by lines $ {\displaystyle{x = y}}$, $ {\displaystyle{x = -y}}$, $ {\displaystyle{x = -1}}$ & $ {\displaystyle{x = 1}}$. 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
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 $ {\displaystyle{(x,y)}}$ in the plane, which satisfy $ {\displaystyle{|y| {\le} |x| {\le} 1}}$.
$ {\displaystyle{|y| {\le} |x| {\le} 1}}$ region will bounded by lines $ {\displaystyle{x = y}}$, $ {\displaystyle{x = -y}}$, $ {\displaystyle{x = -1}}$ & $ {\displaystyle{x = 1}}$. 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
Therefore the final region is the following shaded region:
