Does this function have a discontinuity at $x = 0$? \\ $f(x) = \frac{|x|}{x}$
Added by Ismael W.
Close
Step 1
In this case, the function is f(x) = k√x. First, let's check if the function is defined at x = 0. Since the square root function is defined for non-negative values of x, the function is defined at x = 0. Show more…
Show all steps
Your feedback will help us improve your experience
Carson Merrill and 71 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
See Exercises 95-96. a. Does the function $f(x)=x \sin (1 / x)$ have a removable discontinuity at $x=0 ?$ b. Does the function $g(x)=\sin (1 / x)$ have a removable discontinuity at $x=0 ?$
Limits
Continuity
Do removable discontinuities exist? a. Does the function $f(x)=x \sin (1 / x)$ have a removable discontinuity at $x=0 ?$ Explain. b. Does the function $g(x)=\sin (1 / x)$ have a removable discontinuity at $x=0 ?$ Explain.
Find all points of discontinuity of $f$, where $f$ is defined by $$ f(x)=\left\{\begin{array}{c} \frac{|x|}{x}, \text { if } x \neq 0 \\ 0, \quad \text { if } x=0 \end{array}\right. $$
Continuity and Differentiability
Introduction
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD