How do you prove that the function #1/x# is continuous at x=1?

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Answer 1 · 2016-09-27T12:54:00

See the Explanation.

To prove that a fun. #F(x)# is continuous (cont.) at

#x=a, a in D_F"=the Domain of "F#, we have to prove that,

#lim_(xrarra) F(x)=F(a)#.

So, in our case, we have,

#lim_(xrarr1) f(x)#

#=lim_(xrarr1) 1/x#

#=1/1=1#.

#f(1)=1#.

Thus, #lim_(xrarr1) f(x)=f(1)#.

Hence, #f# is cont. at #x=1#.