- #1

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Cutting a long story short, at some point I needed to calculate the right asymptote of this function:

A(t) = Ln(k⋅t) - k⋅t

where k,t ∈ℝ

^{+}.

The derivative of A(t) tends to -k for t→∞, so I thought the right asymptote would be a line:

B(t)= m⋅t +q

with slope m = -k.

I went on to calculate the intercept q by the usual method, i.e. limit of A(t) + k⋅t for t→∞, and it turned out that it didn't exist (it said it was infinite)!

Is there any mistake in my calculations?

How can a curve have a finite, constant derivative for t→∞, suggesting that it approaches a line, but no intercept?

Tx

L