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

To prove that a fun. F(x) is continuous (cont.) at x = a , a ∈ D F =the Domain of F we have to prove that, lim x → a F ( x ) = F ( a ) So, in our case, we have, lim x → 1 f ( x ) = lim x → 1 1 x = 1 1 = 1 f ( 1 ) = 1 Thus, lim x → 1 f ( x ) = f ( 1 ) Hence, f is cont. at x=1.

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Antwan Perez

Answered question

2022-10-12

How do you prove that the function

\frac{1}{x}

is continuous at x=1?

Answer & Explanation

Layton Leach

Beginner2022-10-13Added 15 answers

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_{x \to a} F (x) = F (a)

So, in our case, we have,

lim_{x \to 1} f (x)

= lim_{x \to 1} \frac{1}{x}

= \frac{1}{1} = 1

f (1) = 1

Thus,

lim_{x \to 1} f (x) = f (1)

Hence, f is cont. at x=1.

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