Question | AP Tutor

40. Consider the functions \( f(x) = \frac{1}{x}, x \ne 0 \), and \( g(x) = x \sin \frac{1}{x}, x \ne 0 \). Which of the following describes the behavior of \( f \) and \( g \) as \( x \to 0 \)?

\( \lim\limits_{{x \to 0}} f(x) = 0 \) and \( \lim\limits_{{x \to 0}} g(x) = 0 \)

\( \lim\limits_{{x \to 0}} f(x) \) and \( \lim\limits_{{x \to 0}} g(x) \) do not exist.

\( \lim\limits_{{x \to 0}} f(x) = 0 \) and \( \lim\limits_{{x \to 0}} g(x) \) does not exist.

\( \lim\limits_{{x \to 0}} f(x) \) does not exist and \( \lim\limits_{{x \to 0}} g(x) = 0 \)

Answer is: option4

\( \lim\limits_{{x \to 0}} f(x) \) does not exist and \( \lim\limits_{{x \to 0}} g(x) = 0 \)

Solution:

Previous Next

AP Calculus AB Tags

AP Calculus BC Tags