Question

using l'hopital's rule, how do I solve for the denominator of the function sin(x)/(x^1/2)) as x approaches 0+? i know that the value of the limit is zero and the numerator is cos(x) but i can't figure out the denominator

Answer 1

(x^n)' = nx^(n-1)

Answer 2

\[\frac d{dx}x^{\frac12}=\frac12x^{-\frac12}=\frac1{2\sqrt x}\]

Answer 3

I tried that for the answer but for some reason it wouldn't work.

Answer 4

That makes it all the more important that you show us your own work. We could then spot any problem and give you appropriate feedback a lot better and faster that way.

Answer 5

Okay so the question is...

Based on your knowledge of the behavior of the numerator and denominator, predict the value of the limit x->0+ sin(x)/(x^1/2)), which I know is 0.

Then the second part asks...Find the limit using l'Hopital's rule: lim x->0+ sin(x)/(x^(1/2)=???? I already have two parts of the answer correct and the denominator I can't solve:

lim x->0+ cos(x)/???? = 0

Answer 6

Your expression is\[\frac{ \sin x }{ x ^{1/2} }. \] I trust you know that to apply l'Hopital's Rule, you need to differentiate the numerator and denominator separately. We don't "solve" the denominator, Lady; we differentiate it. Important distinction! Mind showing your work? Why not use either Equation Editor or Draw for this purpose?

Answer 7

Drawing is better I suppose, but choose what you like :)