Given that the tangent line to the graph of at (0,0) has equation and that has a horizontal asymptote at with equation , find the value of

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- Dec 7th 2007, 04:52 AMpolymeraseLimit...using given info
Given that the tangent line to the graph of at (0,0) has equation and that has a horizontal asymptote at with equation , find the value of

- Dec 7th 2007, 05:35 AMtopsquark
I'm not any sort of an expert at limits, but this looks (Cool) so I'm going to take a shot at it.

First since we know that

Thus

Next we have . We know that since the tangent line to y = f(x) at x = 0 is 2y = x. Thus the limit is of the form and we may apply L'Hopital's rule:

(Because near x = 0.)

Thus

-Dan - Dec 7th 2007, 05:53 AMpolymerase
- Dec 7th 2007, 06:17 AMtopsquark
- Dec 7th 2007, 06:41 AMpolymerase