Determine at which positive values the delta of the inequality [tex]0\ \textless \ |x-x_0|\ \ \ \textless \ [/tex] ẟ inequality follows [tex]|f(x)-a|\ \ \ \t
Mathématiques
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Question
Determine at which positive values the delta of the inequality [tex]0\ \textless \ |x-x_0|\ \ \ \textless \ [/tex] ẟ inequality follows [tex]|f(x)-a|\ \ \ \textless \ [/tex] ε, if:
а)
[tex]f(x)=\frac{x^{2} -4x+3}{x^{2} -2x-3}[/tex]
[tex]x_0=3\\a=\frac{1}{2} \\[/tex]
ε=0,01
б)
[tex]f(x)=sin(x)\\x_0=\frac{\pi }{2} \\a=1\\[/tex]
ε=0,01
в)
[tex]f(x)=sign(x)\\x_0=0\\a=1\\[/tex]
ε=1,5
а)
[tex]f(x)=\frac{x^{2} -4x+3}{x^{2} -2x-3}[/tex]
[tex]x_0=3\\a=\frac{1}{2} \\[/tex]
ε=0,01
б)
[tex]f(x)=sin(x)\\x_0=\frac{\pi }{2} \\a=1\\[/tex]
ε=0,01
в)
[tex]f(x)=sign(x)\\x_0=0\\a=1\\[/tex]
ε=1,5