Ant on a stretchy rope puzzle

[Gavran]

In the general case, the time that the ant needs to reach the end of the rope is $$ T=\frac cv(e^\frac v\alpha-1) $$, where $c$ is the initial length of the rope, $v$ is the rate at which the rope stretches, and $\alpha$ is the speed of the ant relative to the rope.
Clearly, any positive real values of $c$, $v$, and $\alpha$ will always return the positive real value of $T$, which means that the ant will always reach the end of the rope no matter what positive real values are assigned to $c$, $v$, and $\alpha$.

 

[DaveC426913]

In the general case, the time that the ant needs to reach the end of the rope is $$ T=\frac cv(e^\frac v\alpha-1) $$, where $c$ is the initial length of the rope, $v$ is the rate at which the rope stretches, and $\alpha$ is the speed of the ant relative to the rope.
Clearly, any positive real values of $c$, $v$, and $\alpha$ will always return the positive real value of $T$, which means that the ant will always reach the end of the rope no matter what positive real values are assigned to $c$, $v$, and $\alpha$.

Google is too dumb to solve this. It returns undefined.

(1000 / 1000) * (e^(1000 / .01) - 1) = undefined

 

[Ibix]

Google is too dumb to solve this. It returns undefined.

(1000 / 1000) * (e^(1000 / .01) - 1) = undefined

It's obviously well approximated by $e^{100000}$. Noting that $e\approx 10^{0.434}$ this is $(10^{0.434})^{100000}\approx 10^{43400}$. That is rather larger than the maximum value of a double precision variable, which is what Google is probably using.