Question

f(x)=\frac{7}{x}
removable discontinuities x = dne
nonremovable discontinuities x = 0

Explanation:

Step1: Identify discontinuity location

Denominator zero at \( x=0 \).

Step2: Check limit at \( x=0 \)

\(\lim_{x \to 0} \frac{7}{x}\) does not exist (infinite).

Step3: Classify discontinuity

Nonremovable (infinite discontinuity). No removable discontinuities.

Answer:

removable discontinuities: DNE, nonremovable discontinuities: \( x = 0 \)