Continuity In a Function's Domain...1

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Calculus
Section 2.5

I am not going to state any of the theorems as requested here. What does it mean for a function to be continuous in its domain? I forgot how to find the domain of function, which is a Precalculus idea. You can decide which two questions from the problems listed here to answer.

Thank you.

Screenshot_20220516-084133_Samsung Notes.jpg
 
The domain of a rational function consists of all the real numbers x except those for which the denominator is 0 . To find these x values to be excluded from the domain of a rational function, equate the denominator to zero and solve for x .

27,
upload_2022-5-16_17-9-40.gif


domain: R (all real numbers) (since denominator sqrt(x^4+2), no matter what you choose for x, x^4+2 will never be =-2)

graph:
MSP119211d44f2g91521ca500002f882549a4cb2fhf
as you can see, the function is continuous at every number in its domain
 
The domain of a rational function consists of all the real numbers x except those for which the denominator is 0 . To find these x values to be excluded from the domain of a rational function, equate the denominator to zero and solve for x .

27,
View attachment 3094

domain: R (all real numbers) (since denominator sqrt(x^4+2), no matter what you choose for x, x^4+2 will never be =-2)

graph:
MSP119211d44f2g91521ca500002f882549a4cb2fhf
as you can see, the function is continuous at every number in its domain

Thank you very much. I like this set of questions. It has a little Precalculus. How about doing 32 as a guide for me to do a few more? I will show math work on my days off.
 

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