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44*e^(kt/5)+49((1-e^(kt/5))/k)

and I'm supposed to evaluate as k-->0

I think I'm supposed to apply l'hospital's rule to the second part of the equation, which would give

49*((1-t/5*e^(kt/5))/1)

which as k-->0 is

49*(1-t/5)

so the whole thing as k-->0 is

44+49*(1-t/5)

This isn't right, and I also tried l'hosital's rule on the first part of A, which would give 44*t/5 and this isn't right either.

What am I doing wrong?

Thanks.

Here's the whole question, in case I'm not reading it right:

Find the limit of this velocity for a fixed time t_0 as the air resistance coefficient k goes to 0.