Question

Question #e54e5

Answer 1

See the Discussion in Explanation Section.

Explanation:

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

`F` on the interval `[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!