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 x2x\neq 2. Then for b2b\neq 2;

f(x)f(b)asxb.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 x0+x\rightarrow 0+.