Home page for accesible maths Math 101 Chapter 2: Functions of a real variable

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2.14 Example

2.14 Examples

(i) Let f⁢(x)=1/(x-2)f(x)=1/(x-2) for x≠2x\neq 2. Then for b≠2b\neq 2;

f⁢(x)→f⁢(b) as x→b.f(x)\rightarrow f(b)\quad{\hbox{as}}\quad x\rightarrow b.

(ii) Let g⁢(x)=xg(x)=\sqrt{x} for x>0x>0. Then g⁢(x)→0g(x)\rightarrow 0 as x→0+x\rightarrow 0+.