Question Solved1 Answer please use graph to prove that d_r(x) is subset of set A. and set A is a open set that is a triangle, not a quarter circle. 3. Let A = {(x1, x2) E R² | x1, x2 > 0, x1 + x2 < 1}. Show that every point T E A is an interior point of A. Use the definition of interior point. Hint: you need to find a radius r > 0, which will depend on the point ž, such that D,(ã) CA.
DHDWKG The Asker · Calculus
please use graph to prove that d_r(x)
is subset of set A. and set A is a open set that is a triangle, not
a quarter circle.
Transcribed Image Text: 3. Let A = {(x1, x2) E R² | x1, x2 > 0, x1 + x2 < 1}. Show that every point T E A is an interior point of A. Use the definition of interior point. Hint: you need to find a radius r > 0, which will depend on the point ž, such that D,(ã) CA.
More Transcribed Image Text: 3. Let A = {(x1, x2) E R² | x1, x2 > 0, x1 + x2 < 1}. Show that every point T E A is an interior point of A. Use the definition of interior point. Hint: you need to find a radius r > 0, which will depend on the point ž, such that D,(ã) CA.
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A given A={(x_(1),x_(2))inR^(2):x_(1),x_(2) > 0x_(1)+x_(2) < 1}Since x_(1)+x_(2) < 1{:[=>-x_(1) < 1" and "x_(2) < 1" st "x_(1)+x_(2) < 1],[=>0 < x_(1) < 1" and "0 < x_(2) < 1quad" st "x_(1)+x_(2) < 1]:}Interior Point' rarrquad(x_(1),x_(2))in A is called an interior Point If rarr an open Ball B_(epsi)(x_(1),x_(2)) around (x_(1),x_(2)) st(x_(1)//x_(2)) ... See the full answer