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Answer 1 · 2016-08-07T18:23:01

See the Discussion in Explanation Section.

In the first instance, to study the continuity of the given function

$F$ $F$ on the interval $[1, 5]$ $[1,5]$ , there is no need to find $lim_(xrarr1^-)F(x)$ ,

because, by Defn., for $F$ to be continuous on $[1,5]$ ,

we must have,

$(1) : F$ must be cont. at $x=1$ from Right Hand Side , i.e.,

$lim_(xrarr1^+) F(x)=F(1)$ ,

$(2) : F$ must be cont. on $(1,5)$ , and, finally,

$(3) : F$ must be cont. at $x=5$ from Left hand Side , i.e.,

$lim_(xrarr5^-) F(x)=F(5)$ .

Secondly, let us observe that we are not given the defn. of

$F$ for $x<1$ , and, so, we can not discuss its any type of

behavior for $x<1$ .

I hope the above will make the things clear. By the way, I presume, we are in no need to discuss the continuity of $F$ on $[1,5]$ .

Enjoy maths!