L'Hopital's rule..any simple explanation

[RNtoPharmD]

I took calculus years ago and have trouble understanding this rule and also the limit.

Why lim x-->4 of (x^4-256)/(x-4) = 256

or lim x--> ln(2+x)/(x+1) = 1 ???

Basically, you just take derivatives repeatedly until you find the answer ..right?

The study guide is confusing

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[pcproduct]

I just learned L'Hopital's rule today. Your first problem is definitely correct. I can't confirm the second because my class has never gone over the derivative of natural logarithms.

 

[Toomeke]

ln(x) = 1/x

so ln[(2+x)/(x+1)] = (x+1)/(2+x)

multiply top and bottom each by 1/x and you get 1/1 b/c (x/x)/(x/x) = 1/1 = 1

remember that 1/x and 2/x each ->0 as x->infinity

hope that helps.

 

[pharmacyanalyst]

this seems like a good website

http://archives.math.utk.edu/visual.calculus/3/lhospital.1/

 

[Pharmacyguy4]

We have to know L'Hospital's rule for the pcat? I don't remember doing that in Calc I but I know we did that in calc II??

 

[Tatodotcom]

I know this is old but i stumbled upon it....if anyone is interested. app l'hop's rule(which i learned in calc 1) to the first problem to get the answer. and as for the second problem, apply l'hop again then the powers of x are the same on the denominator and numerator, then the limit goes to the coeifficent(1/1).