Homework Statement
Use L'Hopital's rule to evaluate the limit:
lim (x/(x+1))^x
x>infinite
Homework Equations
The Attempt at a Solution
I put it into a logarithm first to make it the limit of xln(x/(x+1)) then I took the derivative and got [(1/x)-(1/(x+1))]/[x^-2]
but its still...
Homework Statement
(a) Explain why L'Hopital's rule does not apply to the problem
lim_{x\rightarrow0} [ (x^{2}sin(1/x)) / sinx ]
(b) Find the limit.
Homework Equations
lim _{x\rightarrow0} xsin(1/x) = 0 , by the Squeezing Theorem.
lim _{x\rightarrow0} sin (1/x) Does Not Exist...
I'm suppose to find the limit as x goes to infinity of [(9x + 1) ^ (1/2)] / [(x+1) ^ (1/2)].
L'Hopital's Rule does not work on here (it said so even in the directions) as the function keeps on cycling.
...they gave us the answer (3) but I need to find out how.
:S
I would like to know if I did these the correct way.
Homework Statement
1.lim x->0 (1/sin 2x)-1/2x. the answer is 0.
2.lim x->0 (x^-5*ln x). The answer is -infinity.
Homework Equations
1.I used L'Hopitals theorem
2.I derived them, than L'hopitals.
The Attempt at a Solution
1.I...
Im trying to solve this problem using l'hopital but amm not sure how to do it
lim
X->infinite x^3 * e^(-x^2)
soo this infinite * e^-infinite... but from there I am not sure if you can use it to solve this...
L'Hopital's Rule - I'm loosing my hair!
Ok, I have the following:
Lim x->0 sqrt(4-x^2) -2 /x
After I change the equation to remove the radicle, I get:
Lim x->0 ((4-x^2)^1/2 - 2)/x
but when I apply the rule the, I'm loosing it I thought I should get:
1/2 ((4-x^2)^-1/2 times...
Homework Statement
lim as x->0 (tan(x)-x)/(sin2x-2x)
Homework Equations
L'Hopitals rule states that if the limit reaches 0/0, you can take the derivative of the top and the bottom until you get the real limit.
The Attempt at a Solution
(sec^2(x)-1)/(2cos2x-2) still 0/0...
evaluate the limit as x=>0 of sqrt(x^2+x) - x
so i multiplied by the conjugate to get:
x^2 + x - x^2 / sqrt(x^2 +x) + x
which simplifies to:
x / sqrt (x^2 + x) + x = infinity/infinity
taking LH, you get:
1 / 1/2(x^2+x)^(-1/2) * (2x+1) + 1 = infinity/infinity again
looking...
Hey,
So I'm having a bit of difficulty with two of these L'Hospital's Rule problems... The first:
\mathop {\lim }\limits_{x \to \infty} (\sqrt{x^2 + x} - x)
So when you have an indefinite form \infty - \infty, you've got to turn it into a product indefinite form, usually something like \infty...
Hi. Use L'Hopital's Rule to evaluate the limit.
lim x-infinity of (lnx) ^(2/x)
The answer is 1.
I kept taking the derivative but it seemed like I was going around in circles. Any help would be appreciated.
Thanks
I am trying to work through the following problem:
if function is differentiable on an interval containing 0 except possibly at 0, and it is continuous at 0, and 0= f(0)= lim f ' (x) (as x approaches 0). Prove f'(0) exists and = 0.
I thought of using the definition of a limit to get to lim [...
Having trouble with a question on L'Hopital's rule. I have never come across it must have misseda lecture. From what I understand the rule approximates values at a limit. Here's what I have anyway.
I've derived a velocity gradient for a spherically symmetric, isothermal stellar wind as...