Property 17
Limit of Sign Function
\(a\in\mathbb R\)
\(f(x)=\operatorname{sgn}(g(x))\)
\(g(a)=0\)
a point is the critical point of f function. In the critical point left-hand and right-hand functions are analyzed. On the other points function is continuous.
1.
\(\lim\limits_{x\to5}\operatorname{sgn}(x-1)=?\)
2.
\(\lim\limits_{x\to2}\operatorname{sgn}(x-5)=?\)
3.
\(\lim\limits_{x\to3^-}\operatorname{sgn}(x-3)=?\)
4.
\(\lim\limits_{x\to-2^+}\operatorname{sgn}(x+2)=?\)
5.
\(\lim\limits_{x\to-1^-}\operatorname{sgn}(x^2-1)=?\)
6.
\(\lim\limits_{x\to3}(|x-2|\cdot\operatorname{sgn}(x-3))=?\)
7.
\(\lim\limits_{x\to4^+}\samefrac{\operatorname{sgn}(x-4)}{|x^2-2|}=?\)
8.
\(\lim\limits_{x\to2^+}\samefrac3{\operatorname{sgn}(x^2-4)}=?\)
9.
\(\lim\limits_{x\to2}\samefrac{\operatorname{sgn}(x-2)}{\operatorname{sgn}(2-x)}=?\)
10.
\(\lim\limits_{x\to0}(\operatorname{sgn}(x^2))=?\)
11.
\(\lim\limits_{x\to\pi^+}(\operatorname{sgn}(\sin x))=?\)
12.
\(\lim\limits_{x\to\samefrac\pi2}\operatorname{sgn}(\cos x)=?\)