Math Problem Statement
As x gets closer and closer to (but stays less than) 1 , g(x) gets as close as we want to …
Solution
As approaches 1 from the left (i.e., ), the graph of the function tends towards a value. Observing the curve of , it appears that the function approaches the value 3 from the left side of .
Therefore, as gets closer and closer to 1 from the left (but remains less than 1), gets as close as we want to 3.
Would you like any further clarification or details on this?
Here are 5 related questions you might want to explore:
- What happens to as approaches 1 from the right?
- Is continuous at ?
- How do you calculate one-sided limits from graphs?
- What is the limit of as approaches 3?
- How can you describe the behavior of for large negative values of ?
Tip: When analyzing limits graphically, always check for discontinuities and consider both the left-hand and right-hand
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Math Problem Analysis
Mathematical Concepts
Limits
One-Sided Limits
Graph Analysis
Formulas
Limit notation: \( \lim_{x \to c^-} g(x) \)
Theorems
One-Sided Limit Theorem
Suitable Grade Level
Grades 10-12