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hms.tech
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The function f is continuous at some point c of its domain if the limit of f(x) as x approaches c through the domain of f exists and is equal to f(c). In mathematical notation, this is written as
[itex]lim_{x\rightarrow c}[/itex] f(x) = f(c) from the positive and negative sides .
For ln(x) (the natural log of x), as x[itex]\rightarrow[/itex]0 , ln(x) approaches -[itex]\infty[/itex]
Hence I would stand by the notion that ln(x) is not continuous since at x=0, the function is not defined .
Also, the graph does not exist in x<0 domain ; so ln(x) can never approach -[itex]\infty[/itex] from the -ve "x" side .
[itex]lim_{x\rightarrow c}[/itex] f(x) = f(c) from the positive and negative sides .
For ln(x) (the natural log of x), as x[itex]\rightarrow[/itex]0 , ln(x) approaches -[itex]\infty[/itex]
Hence I would stand by the notion that ln(x) is not continuous since at x=0, the function is not defined .
Also, the graph does not exist in x<0 domain ; so ln(x) can never approach -[itex]\infty[/itex] from the -ve "x" side .