Show that ( f(x)=left{egin{array}{ll}left(x^{2} / a ight)-a & x leq a \ a-left(a^{2} / x ight) & x>aend{array} ight. ) is continuous at ( x=a ).
Added by Chandrakant G.
Close
Step 1
Step 1: We need to show that the limit of the function as x approaches a from the left is equal to the limit of the function as x approaches a from the right, and both of these are equal to the value of the function at x = a. Show more…
Show all steps
Your feedback will help us improve your experience
Supratim Pal and 76 other Algebra 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
Show that the function $ f $ given by $ f(x) = | x | $ is continuous on $ \mathbb{R}^n $. [ $ \textit{Hint:} $ Consider $ | x - a |^2 = (x - a) \cdot (x - a) $.]
Partial Derivatives
Limits and Continuity
If $f(x)$ is continuous at $x=a,$ prove that $g(x)=|f(x)|$ is continuous at $x=a.$
Continuity and its Consequences
Let $$f(x)=\left\{\begin{aligned} A^{2} x^{2}, & x \leq 2 \\ (1-A) x, & x>2 \end{aligned}\right.$$ For what values of $A$ is $f$ continuous at $2 ?$
Continuity
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD