Let L be a real number. For functions f and g defined on the set of real numbers, $$\lim _ { x \rightarrow 2 } f ( x ) = \lim _ { x \rightarrow 2 } g ( x ) = L$$ equality is satisfied. Accordingly, I. $f ( 2 ) = g ( 2 )$ II. $\lim _ { \mathrm { x } \rightarrow 2 } ( \mathrm { f } ( \mathrm { x } ) - \mathrm { g } ( \mathrm { x } ) ) = 0$ III. $\lim _ { x \rightarrow 2 } \frac { f ( x ) } { g ( x ) } = 1$ Which of the following statements are always true? A) Only I B) Only II C) I and III D) II and III E) I, II and III
Let L be a real number. For functions f and g defined on the set of real numbers,
$$\lim _ { x \rightarrow 2 } f ( x ) = \lim _ { x \rightarrow 2 } g ( x ) = L$$
equality is satisfied.
Accordingly,
I. $f ( 2 ) = g ( 2 )$
II. $\lim _ { \mathrm { x } \rightarrow 2 } ( \mathrm { f } ( \mathrm { x } ) - \mathrm { g } ( \mathrm { x } ) ) = 0$
III. $\lim _ { x \rightarrow 2 } \frac { f ( x ) } { g ( x ) } = 1$
Which of the following statements are always true?
A) Only I
B) Only II
C) I and III
D) II and III
E) I, II and III