# Solve A: Evaluating L'Hospital's Rule for k→0

• glid02
In summary, the conversation revolves around evaluating the limit of a given equation as k approaches 0. The speaker mentions applying l'Hospital's rule to both parts of the equation, but their results are incorrect. The correct result using l'Hospital's rule on the second part is 49*(1-t/5) as k approaches 0. The question is then clarified and the correct answer is given as -49/5*t.

#### glid02

I have the equation A
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.

You have, by L'Hopital's rule:
$$\lim_{k\to{0}}49\frac{1-e^{\frac{kt}{5}}}{k}=\lim_{k\to{0}}49\frac{-\frac{t}{5}e^{\frac{kt}{5}}}{1}=-\frac{49}{5}t$$

Oh yeah, that 1 should've disappeared from what I found.

Thanks a lot.

## 1. What is L'Hospital's Rule?

L'Hospital's Rule is a mathematical tool used to evaluate limits of indeterminate forms, where both the numerator and denominator approach zero or infinity.

## 2. When should L'Hospital's Rule be used?

L'Hospital's Rule should be used when evaluating limits of indeterminate forms, such as 0/0 or ∞/∞. It cannot be applied to other types of limits.

## 3. How do you apply L'Hospital's Rule?

To apply L'Hospital's Rule, take the derivative of the numerator and denominator separately and then evaluate the limit again. This process can be repeated multiple times if necessary.

## 4. What is k→0 in L'Hospital's Rule?

k→0 represents the variable k approaching the value of 0. This means that as k gets closer and closer to 0, the limit is being evaluated.

## 5. Are there any limitations to using L'Hospital's Rule?

Yes, there are limitations to using L'Hospital's Rule. It can only be applied to certain types of limits and may not always give the correct answer. Additionally, it should be used with caution and only as a last resort when other methods of evaluating the limit have failed.