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As I read in the James Stewart's Calculus 7th edition, he said:

My question is: Is [itex]f(x)\rightarrow 0[/itex] the same as [itex]f(x) = L[/itex]?

For example,

[itex]f(x) = x^2[/itex]

[itex]\displaystyle\lim_{x\rightarrow 5}f(x) = 25[/itex]

I can say that [itex]f(x) = x^2[/itex] approaches 25 as [itex]x[/itex] approaches 5.

Therefore, can I say that the f(x) is not equal to 25 unless x is not approaching 5, but x, itself, is 5?

Thanks for reading!!!

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An alternative notation for

[itex]\displaystyle\lim_{x\rightarrow a}f(x) = L[/itex]

is

[itex]f(x) \rightarrow L[/itex] as [itex]x \rightarrow a[/itex]

which is usually read "f(x) approaches L as x approaches a"

My question is: Is [itex]f(x)\rightarrow 0[/itex] the same as [itex]f(x) = L[/itex]?

For example,

[itex]f(x) = x^2[/itex]

[itex]\displaystyle\lim_{x\rightarrow 5}f(x) = 25[/itex]

I can say that [itex]f(x) = x^2[/itex] approaches 25 as [itex]x[/itex] approaches 5.

Therefore, can I say that the f(x) is not equal to 25 unless x is not approaching 5, but x, itself, is 5?

Thanks for reading!!!

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