Science:Math Exam Resources/Courses/MATH110/December 2017/Question 05 (a)

MATH110 December 2017

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Question 05 (a)
(a) List the conditions that a function ${\textstyle f(x)}$ must satisfy in order to be continuous at ${\textstyle x=a}$.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Consider the left hand limit, the right hand limit, as well as the value of the function at the point.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. Recall the definition, we need the following conditions: the left hand limit ${\textstyle \lim \limits _{x\to {a}^{-}}f(x)}$ exists; the right hand limit ${\textstyle \lim \limits _{x\to {a}^{+}}f(x)}$ exists; the functional value ${\textstyle f(a)}$ is defined; the above three values are equal. Answer: the conditions are that ${\textstyle {\color {blue}\lim \limits _{x\to {a}^{-}}f(x),\,\lim \limits _{x\to {a}^{+}}f(x),\,f(a){\mbox{ all exist and are equal}}}}$.