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Let us say that we have a graph f(x)=2x when x does not equal 3, and f(x)=undefined when x=3

The limit of f(x) as x→3, is still 6.

But what about the limit of 3+dx? Does it exist?

I am not up to the derivatives section of my class, so maybe there is something I am not understanding yet.

Because 3+dx is the smallest possible number after 3...and the limit of 3+dx=2(3+dx)=6+dx, if you just plug it in to the function. But, immediately to the left of 3+dx, f(x) is not defined, so the graph isn't getting closer and closer to 3+dx as you approach it from the left hand side...because the graph is actually getting closer and closer to being undefined.

So would the limit not exist for 3+dx in this example?

Thanks

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# Question about limits

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