Need help with lim (L'Hopital)

[pedrosi07]

Question from Howard Anton book (A New Horizon-Vol 1):
Find all values for K and L
lim x->0 of K+cosLx/x^2 = -4
Couldn't move one step forward.

 

[ksdhart]

Before I can help you, I need to know exactly what the problem you're working on is. What you wrote is very ambiguous. For example, is your problem:

$\displaystyle \lim _{x\to 0}\left(K+\frac{cos\left(Lx\right)}{x^2}\right)=-4$

Or is it:

$\displaystyle \lim _{x\to 0}\left(K+cos\left(\frac{Lx}{x^2}\right)\right)=-4$

Or something else entirely? Unless I know what problem you're doing, I can't even suggest a first step.

 

[Ishuda]

Question from Howard Anton book (A New Horizon-Vol 1):
Find all values for K and L
lim x->0 of K+cosLx/x^2 = -4
Couldn't move one step forward.

I strongly suspect it is
$\displaystyle \underset{x\to0}{lim} \frac{K\, +\, cos(Lx)}{x^2}\, =\, -4$
if K and L as supposed to be constants.

If that is the case, then since L'Hopital's Rule is for zero over zero or (plus or minus) infinity over infinity and the denominator is going to zero, that would mean the numerator would have to go to zero to use L'Hopital's Rule. What does K have to be for the numerator to go to zero as x goes to zero? Given that value of K, apply L'Hopital's Rule twice to obtain the values for L.