What Are the Properties of Limits for Basic Functions?

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SUMMARY

The discussion focuses on the properties of limits for basic functions, specifically evaluating limits involving functions h(x), f(x), and g(x) with values lim h(x) = 0, lim f(x) = -5, and lim g(x) = 9. The participants confirm the correctness of various limit operations, including addition, subtraction, multiplication, and division. Key conclusions include that lim sqrt(f(x)) does not exist due to the square root function being undefined for negative inputs, and that the limit of 1/f(x) - g(x) can be evaluated using established limit rules.

PREREQUISITES
  • Understanding of limit properties in calculus
  • Familiarity with basic functions and their behaviors
  • Knowledge of operations involving limits (addition, subtraction, multiplication, division)
  • Concept of limits approaching infinity or non-existence
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  • Study the formal definition of limits in calculus
  • Learn about the continuity of functions and its impact on limits
  • Explore the concept of limits involving indeterminate forms
  • Investigate the application of L'Hôpital's Rule for evaluating limits
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Students studying calculus, educators teaching limit concepts, and anyone seeking to deepen their understanding of mathematical analysis involving limits of functions.

asdfsystema
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hey guys, thanks for taking the time to check over my answers !

lim h(x)= 0 lim f(x)= -5 lim g(x) = 9

1. lim h(x)+f(x)= -5
2. lim h(x)-f(x) = +5
3. lim h(x)*g(x)= 0
4. lim h(x)/f(x) = 0
5. lim h(x)/g(x)= 0
6. lim g(x)/h(x) = DNE
7. lim squareroot (f(x)) = DNE (?)
8. lim f(x)^-1 = -1/5 ?
9. lim 1/ f(x) - g(x) = -1/14?

Thanks in advance please help me check over my answers !
 
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Yes, those are all correct. I am assuming you meant a brackets around the f(x) - g(x) on your last one. From the ?'s on your last 3 I am assuming you aren't too sure about them.

7. Does not exist as the Sqrt function is not defined in the neighborhood of -5.

8. It's just the same rule you used in 4, but this time its 1 instead of lim h(x) on the numerator.

9. Same rule again - Limit of the whole thing is limit of the top over the limit of the bottom. And the limit of the bottom just uses the rule you used in 2.
 
thank you ! you're right =)
 

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