L'hopital's rule Definition and 115 Threads

Homework Statement \displaystyle\lim_{x\rightarrow 0^+} \frac{e^x - (1 + x)}{x^n} where n is a positive integer The Attempt at a Solution The numerator approaches 0 as x approaches 0 from the right. The denominator approaches 0 with whichever positive integer, n. This gives an...

The rule states that: { lim }_{ x\rightarrow c }\quad \frac { f(x) }{ g(x) } \quad =\quad { lim }_{ x\rightarrow c }\quad \frac { f'(x) }{ g'(x) } Right? So if { lim }_{ x\rightarrow 2 }\frac { { x }^{ 2 }+1 }{ x-1 } \quad =\quad 5 Then shouldn't { lim }_{ x\rightarrow...

I've been reading over the l'Hopital's rule proof here: http://www.math.uga.edu/~pete/2400diffmisc.pdf For the first case of the proof, how does f(x)/g(x) <α imply the limit as x -> a is also A? I understand that α is an arbitrary number greater than A, which means that the limit is less...

I just want to know how to fiind the derivative of the denominator. The question is as below: How can I find the limit for [f(x)-cosa]/(x-a) using l'Hopital's rule? Note: when x≠a, f(x)= [sinx-sina]/ (x-a) when x=a, f(x)= cosa So,here's what I know, Since f(x)= cosa, then f(a)=...

How can I find the limit for [f(x)-cosa]/(x-a) using l'Hopital's rule? Note: when x≠a, f(x)= [sinx-sina]/ (x-a) when x=a, f(x)= cosa So,here's what I know, Since f(x)= cosa, then f(a)= cosa and therefore, substituting this into [f(x)-cosa]/(x-a) gives [f(x)-f(a)]/(x-a)...

Homework Statement lim x→∞ of ((x^3+2x-∏)^(1/3))-x Homework Equations L'Hopital's Rule: If it is an indeterminate form, take the derivative of the top and bottom until you do not get an indeterminate form anymore. The Attempt at a Solution lim x→∞ of ((x^3+2x-∏)^(1/3))-x...

Homework Statement \lim_{x\rightarrow2}\frac{x\sqrt{x-1}-2}{x-2} Homework Equations calculate the limit The Attempt at a Solution When I apply l'hopital's i have to do derivative of the top over derivative of the bottom right?

Is that any way to find a finite value which is not equal to zero using L'hopital's rule in limit(z=-ia) exp[-A/(z+ia)]/(z+ia)^2 i kept getting 0/0 after differentiation Thank you

The limit n->infinity I have to compute is:\frac{n\cdot \log ^{5}(n)}{n^{2}}Should I use L'hopital's rule? If I do, I have a problem: First I simplify and get: \frac{ \log ^{5}(n)}{n} Taking the derivative of the top, and the bottom leads to: \frac{\frac{ 5\log ^{4}(n)}{n}}{1} At this...

Homework Statement I know it needs L'Hopital but i can't get it to the indeterminant form Limit (x-(x+2)e^(1/x)) ((inf - inf )) x-->inf I reached until here and then i got stuck (1-((x+2)e^(1/x))/x)/(1/x) (1 -inf/inf)/0

Homework Statement Hey guys. Can I please have some help with this limit over here http://imageshack.us/photo/my-images/839/targil.jpg/ BTW I can't use l'Hôpital's rule. I'm trying to help someone how haven't learned how to Derivative yet. Thanks a lot. Homework...

Homework Statement I have L = \lim_{x\rightarrow 0} \Big( {\frac{\cos(1.92x)-1} {e^{2.33x} - 1 -2.33x}} \Big) I'm meant to use L'Hôpital's rule finding the limit, maybe twice. The Attempt at a Solution So, there's clearly something I have misunderstood, and hoping you might tell...

I understand the use of this rule for the limit as x goes to 0, but not for the limit as x goes to infinity. Can this rule be used to find limits to infinity? How? I have googled this but couldn't find a good explanation.

I should have made the title say "using L'h..." rather than what it is, I apologize. Homework Statement Prove the compounding interest formula from the following: A=A_{0}(a+\frac{r}{n})^{nt} Homework Equations The Attempt at a Solution A=A_{0}(a+\frac{r}{n})^{nt}...

I recently learned about L'Hopital's Rule in calculus and as I was doing some practice problems I came across two that confused me a lot. I was hoping that someone could help me with them here. The problem is lim(t→0)⁡〖(sint)(lnt)〗. I tried to make (sint)(lnt) a quotient by setting the...

Homework Statement limit as n approaches infinity of (ln(1/n) / n) Homework Equations The Attempt at a Solution Would it be valid to exponentiate (not sure if you can make that into a verb or not) the top and bottom, yielding (1/n) / e^n Then, if I take the limit I get...

Homework Statement Use L'Hopital's rule to calculate the following derivatives. Homework Equations 1. lim x-> pie/2 tan3x/tan5x 2. lim x->0 e^x - 1/sin x 3. lim x->1 e^x - e/In x The Attempt at a Solution i have attempted to solve the...

I'm not supposed to get help with the exact problem, but, in general, you what do if this happens?

Homework Statement Find f'(0) given a piecewise function defined as f(x) = {g(x)/x2, x≠0 {0, x=0 where g(x) is a function satisfying g(0)=g'(0)=g''(0) and g'''(0)=14 Homework Equations none. The Attempt at a Solution So far, I've reasoned that for f to be differentiable...

Say you have a limit in indeterminate form (0/0 or infinity/infinity) and you apply L'Hopital's rule to it and the result is an infinite limit. Is that a valid answer? Can L'Hopital's rule be applied in this way?

Homework Statement lim x->0 5x(cos 9x-1)/sin 5x-5x Homework Equations The Attempt at a Solution answer is 243/25 The derivative of sin 5x-5x is always 0, dunno know how to do it...

So I've been working on my analysis homework and I am stuck on the last question! Please help! the question is lim x approaches to 0 of (x/sin x)^1/x^2 the answer is e^1/6 but my l'Hopital's process keeps giving me 0/0... After taking the log of the limit, I have ====>...

Homework Statement L'Hopital's rule does not help with this limit. Find it some other way. lim (squarert(x)/squarert(sinx)) as x -> 0+ Homework Equations None? The Attempt at a Solution The only way I can think of solving this is by using L'Hopital's rule...but it obviously...

I know L'Hoptal's rule can only be use when you have indeterminate forms and such, but I do not know how to make a limit a fraction sometimes. Take this limit for example: The limit at which X approaches infinity of (1+\frac{1}{x})X I make y = The limit at which X approaches infinity of...

Homework Statement lim as x -> 0 sin(e^(x^2)-1)/e^(cosx)-e See Link Below. I saw this on the net and tried to solve it. I'm wondering if I'm correct by any means or did I mess up somewhere along the line. Homework EquationsThe Attempt at a Solution...

Homework Statement Evalutate the limit, as x approaches 0, log(coshx)/x2Homework Equations L'Hopital's ruleThe Attempt at a Solution I can get as far as (sinhx.cosh-1x)/2x by differentiating the top and bottom separately. I'm not sure how to do the next differentiation. Thanks for any help.

Homework Statement lim (sin4x) divided by (x^2+8x) x approaches 0 Homework Equations L'Hopital's rule The Attempt at a Solution u = sin4x du = cos4x y = x^2+8x dy = 2x+c

let f(x) exp(-1/x) for x>0, 0 for x<=0 i want to get f'(x) by using l'hopital's rule, but somehow i'm applying l'hopital's rule again and again and no clear value is coming out. i know f'(0) is 0, but i cannot prove it

Homework Statement Lim tan (x^1/2)/ [x (x+1/2)^1/2 ] x-> 0 The Attempt at a Solution I have attempted to differentiate both the denominator and numerator seperately but this just seems to complicate the whole equations and I still get a limit of 0...

Homework Statement Evaluate the limit analytically if necessary using L’Hopital’s rule: lim x->0 (1+x)1/x Homework Equations The Attempt at a Solution Well, I can get the thing equal to 1 if I just plug in zero, so do I need to use L'hopital's? This whole thing is very confusing...

lim as x approaches 4 from the right of [3(x-4)]^(x-4) when you plug in 4 it becomes a 0^0. So I attempted to manipulate it so it would become a 0/0 form so I could l'hopital it. (sorry if I keep spelling it wrong) so lim(x-4)ln(3x-12)=lny then I l'hopitaled it: lim...

Homework Statement http://img213.imageshack.us/img213/4474/scan0001ha.jpg

The proofs of y = \displaystyle\lim_{x \to\infty} (1 + 1/x)^{x} = e that I have seen basically involve taking the natural log of both sides and getting the equation in a form where L'Hopital's rule can be applied. The problem I have with this is that it requires taking the derivative of the...

The problem statement Using the Equation P(\theta)= P1[ \frac{sin(Nkdsin(\theta)/2)}{sin(kdsin(\theta)/2)} ]2 show that the probability at sin(\theta)=j\frac{\lambda}{d}, where j is an integer, is P(\theta=sin-1(j\lambda/d))=N2P1 Hit: find...

Homework Statement Evaluate \lim_{x\rightarrow0}\frac{e^{-\frac{1}{x}}}{x} The Attempt at a Solution I tried taking logarithms and applying l'Hôpital's rule, but that just led to an expression which diverged, and as far as I understand, the limit in l'Hôpital's rule MUST exist.

Homework Statement What is the value of xln(x)-x when x=0?Homework Equations I'm assuming you do L'Hopital'sThe Attempt at a Solution I'm assuming you factor out the x, leaving: x(ln(x)-1) but that's still not in the form of \frac{\infty}{\infty} or \frac{0}{0} Would you do...

Is there an analog to l'Hopital's rule for functions of more than one variable? Or am I stuck using \epsilon \delta proofs and the squeeze theorem? Those also depend on me knowing the value of the limit beforehand which can be tricky in itself.

I've a question concerning spivak's proof of L'Hopital's rule (in chapter 11). It goes like this, lim (x tends to a) of f = 0 lim (x tends to a) of g = 0 lim (x tends to a) of f'/g' exists, then, lim (x tends to a) f/g exists and is equal to lim (x tends to a) of f'/g' He...

Homework Statement \lim_{x\to +\infty} \frac{x}{\sqrt{x^2+1}} Homework Equations The Attempt at a Solution \lim_{x\to +\infty} \frac{x}{\sqrt{x^2+1}} \stackrel{l'H}{=} \lim_{x\to +\infty} \frac{\sqrt{x^2+1}}{x} \stackrel{l'H}{=} \lim_{x\to +\infty} \frac{x}{\sqrt{x^2+1}}...

The question is: Evaluate the following limit: lim(as x tends to 1) of [(x-1)^3]/(logx) I tried using L'hopital's Rule, so i differentiated the top and bottom of the eqn and i got 3x(x-1)^2, then as x tends to 1 this would tend to 0. I don't think this is correct though, and was wondering...

In my math class lectures at the university while studying multivariable functions the lecturer never mentioned L'hopital's rule for these multivariate functions..But in a tutorial class,a tutorial assistant approached this question..find lim (x,y)-->(0,0) [sin(x^2+y^2)]/(x^2+y^2)..by implicitly...

Homework Statement Find the limit as x->0+ of (ln(x))^x *The answer is 1*Homework Equations l'Hôpital's rule The Attempt at a Solution lim (ln(x))^x = 0^0 I took the ln of that quantity to bring down the x lim = x*ln(ln(x)) lim = ln(ln(x)) / (1/x) Then I used l'Hôpital's rule...

Homework Statement Find the limit as x -> 0+ of (sin x)(ln x) Homework Equations None The Attempt at a Solution I rewrote this as (sin x) / (1/ln x), then using L'Hopital it becomes: (cos x) / [(-ln x) / (ln x)2] = [(ln x)2 cos x] / (-ln x) So I get limit as x -> 0+ of...

Suppose f is defined in a neighborhood of x, and suppose f '' (x) exists. Show that: lim [f(x+h)+f(x-h)-2f(x)] / h^2 = f''(x). h->0 Show by an example that that the limit may exist even if f '' (x) may not. (hint: use lHopital's Theorem). Proof: f '' (x) exists implies...

Okay I wish to try to construct an Epsilon-Delta Definition to prove the L'Hopital's Rule (0/0 form). Please correct me if I am wrong. http://mathforum.org/library/drmath/view/53340.html I found the above site. Scrolling down one would the proof. I can follow how an x constraint is...

I had a test today and there was a LR limit on it that I didn't get. I thought he said he got them out of the book, but I didn't see it anywhere. The equation was: lim x\rightarrow\infty of (1 + cosx(1/x))x So, I said that lim x\rightarrow\infty of cos(1/x) = cos(0) = 1 And therefore...

Homework Statement Hi all, I'm new here, and just have a quick question: Evalute: lim as x\rightarrow\infty of \frac{x - sin x}{x^{3}} Homework Equations l'hopital's rule? The Attempt at a Solution So far I've used L'hopital's rule to get it down to lim as x\rightarrow\infty...

Homework Statement find the limit as x approaches 1- of [(1-x^2)^1/2] / [(1-x^3)^1/2] aka root(1-x^2)/root(1-x^3) Homework Equations The Attempt at a Solution Well I don't really get how to solve this limit using l'hopital's rule if i differentiate both top and bottom i...

It's been a while since I've evaluated limits, and I'm beginning to forget some of the techniques. A problem came up in physics which involved evaluating a limit of this particular form. Homework Statement \lim_{x \to \infty} \left( \frac{x}{\sqrt{x^2+y^2}} \right) Homework Equations...

Homework Statement Find \lim_{x-> \inf} \frac{(8-x)^{200}}{8^{x+2}}*\frac{8^x}{(3-x^2)^{100}} Homework Equations The Attempt at a Solution Simplified to: \lim_{x-> \inf} \frac{(8-x)^{200}}{64(3-x^2)^{100}} Indeterminant form, so I suppose L'hopital's, but it doesn't seem very efficient?