pam93
06.03.2020 •
Mathematics
.7*7Since f(0,0) is undefined, f has a discontinuity at (x,y)=(0,0). Is it possible to define a function g:R2→R such that g(x,y)=f(x,y) for all (x,y)≠(0,0) and g is continuous everywhere? If so, what would the value of g(0,0) be? If there is no continuous function g, enter DNE.
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Ответ:
Let the chord- part of VC inside smaller circle be a, and same of CU be b.
According to intersecting secants theorem we have:
CI * (CI + a) = CJ * (CJ + b)and
VC *(CI + a) = CU * (CJ + b)From the second equation we get:
CU = VC * (CI + a) / (CJ + b)From the first equation we get:
CI + a = CJ * (CJ + b) / CI,substitute this into the second equation:
CU = VC * CJ * (CJ + b) / CI * 1/ (CJ + b)CU = VC * CJ / CICU * CI = VC * CJProved