1. ## L'Hopital

when finding the limit as x approaches zero of a vector, when plugging in zero, I get (1/2)i + 0j + 0k

On my test I wrote the limit is 1/2 but my teacher circled 0j+0k and wrote "use L'Hopital." Does this mean the limit is 0 since two of the three terms go to 0?

2. Originally Posted by cottekr
when finding the limit as x approaches zero of a vector, when plugging in zero, I get (1/2)i + 0j + 0k

On my test I wrote the limit is 1/2 but my teacher circled 0j+0k and wrote "use L'Hopital." Does this mean the limit is 0 since two of the three terms go to 0?
What was the original problem?

3. find the limit as x approaches 0 of [(2x+3)/(x^2+6)]i + [(sin(x)/x]j + [(e^x) -1]k

4. Originally Posted by cottekr
find the limit as x approaches 0 of [(2x+3)/(x^2+6)]i + [(sin(x)/x]j + [(e^x) -1]k
$\displaystyle \lim_{x\to0}\frac{\sin x}{x}=1$, not $\displaystyle 0$.

To see this, use L'Hopital's Rule (because we have the $\displaystyle \frac{0}{0}$ case):

$\displaystyle \lim_{x\to0}\frac{\sin x}{x}=\lim_{x\to0}\frac{\cos x}{1}=1$

So the answer is $\displaystyle \frac{1}{2}\hat{i}+\hat{j}$.