Use the definition of limit to show that lim x rightarrow 1

Use the definition of limit to show that lim x rightarrow 1 1/x = 1.

Solution

LHL:

x -> 1^- => x = 1 - h

lim x -> 1 (1/x) = lim h -> 0 (1/1-h) = 1/1-0 = 1

RHL:

x -> 1⁺ => x = 1 + h

lim x -> 1 (1/x) = lim h -> 0 (1/1+h) = 1/1+0 = 1

since, LHL = RHL

lim x-> 1 (1/x) = 1