could somenone tell me how to prove if these functions are locally (in x) or globally lipschitzian?
a)$f(t,x)=|t|(|tx|)^{1/2}$ b)$f(t,x)=(\frac{1+t}{1+x})^{1/2}$ with $t,x\in]-1,1[$
Thanks.
2026-04-25 03:13:28.1777086808
Question about lipschistzian functions
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Hints: a) Consider $f(1/2,x) - f(1/2,0).$
b) Lipschitz functions on bounded domains are bounded. Is $f$ bounded on this domain?