continuity
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What are the characteristics of a continuous function around a given point?
Please show us what you have tried and exactly where you are stuck.
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HallsofIvy
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Do you know what "function f is continuous at x= a" means? That is obviously a necessity for this problem!
"Function f is continuous at x= a" means that \(\displaystyle \lim_{x\to a} f(x) \ = f(a)\). So the second question is "do you know how to find a limit?". I won't go through the complete definition but you should know that all polynomials are continuous at every a and all rational functions are continuous as long as the denominator is not 0. A rational function can be continuous where the denominator is 0 if the numerator is also. Finally, \(\displaystyle \lim_{x\to 0} \frac{sin(x)}{x}\) is well known- look it up.
"Function f is continuous at x= a" means that \(\displaystyle \lim_{x\to a} f(x) \ = f(a)\). So the second question is "do you know how to find a limit?". I won't go through the complete definition but you should know that all polynomials are continuous at every a and all rational functions are continuous as long as the denominator is not 0. A rational function can be continuous where the denominator is 0 if the numerator is also. Finally, \(\displaystyle \lim_{x\to 0} \frac{sin(x)}{x}\) is well known- look it up.
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