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DaalChawal
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MHB Continuity Problem: Solutions & Resources
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A function is continuous at a point if its limit at that point equals its function value. In the discussion, both the left-hand limit and right-hand limit as x approaches 1 yield 0, confirming that f(1) is also 0, thus establishing continuity at x=1. The conversation shifts to exploring continuity at other integer values of x and identifying any real values where the function may not be continuous. Participants are encouraged to investigate these additional points for continuity. The focus remains on understanding the behavior of the function beyond the established point.
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I like Serena
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A function is continuous at a point if its limit at that point is the same as its function value.
What is $\lim_{x\to 1} f(x)$ and what is $f(1)$?
What is $\lim_{x\to 1} f(x)$ and what is $f(1)$?
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DaalChawal
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I'm getting $f(1)$ as well as $\lim_{x \to 1}f(x)$ = 0 both lhl and rhl
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Then $f$ is continuous at $x=1$ and we have eliminated answer a.DaalChawal said:
The remaining question is what happens at other values of $x$.
Can we find another integer value for $x$ where $f$ is continuous?
Can we find a real $x$ where $f$ is not continuous?
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