use the definition of continuity to determine whether f(x)=x + 16/x - 16 is continuous at 16. is f…

use the definition of continuity to determine whether f(x)=x + 16/x - 16 is continuous at 16. is f continuous at 16? select the correct choice below and, if necessary, fill in the answer boxes to complete your answer choice. a. yes. because f(16)= and lim x→16 f(x)=. b. no. because f(16)= and lim x→16 f(x)=, and f(16)≠lim x→16 f(x). c. no. because f(16) does not exist.

use the definition of continuity to determine whether f(x)=x + 16/x - 16 is continuous at 16. is f continuous at 16? select the correct choice below and, if necessary, fill in the answer boxes to complete your answer choice. a. yes. because f(16)= and lim x→16 f(x)=. b. no. because f(16)= and lim x→16 f(x)=, and f(16)≠lim x→16 f(x). c. no. because f(16) does not exist.

Answer

Explanation:

Step1: Evaluate f(16)

Substitute (x = 16) into (f(x)=\frac{x + 16}{x-16}). We get (f(16)=\frac{16 + 16}{16-16}=\frac{32}{0}), which is undefined.

Step2: Analyze continuity condition

For a function (y = f(x)) to be continuous at (x=a), three - conditions must be met: (f(a)) exists, (\lim_{x\rightarrow a}f(x)) exists, and (\lim_{x\rightarrow a}f(x)=f(a)). Since (f(16)) does not exist, the function is not continuous at (x = 16).

Answer:

C. No. Because f(16) does not exist.