Evaluate the intermediate difference with L'Hospital's rule

  • Thread starter Thread starter Painguy
  • Start date Start date
  • Tags Tags
    Difference
Painguy
Messages
118
Reaction score
0

Homework Statement



limit (x-sqrt(x^2 -1)) x-> inf

Homework Equations





The Attempt at a Solution



What I had in mind was to somehow get rid of the radical so I can factor out an x then use L'Hospital's rule with the resulting intermediate product. I'm not sure how to approach the problem however.
 
Physics news on Phys.org
L'hopital, not L'hospital. LOL.
 
operationsres said:
L'hopital, not L'hospital. LOL.

http://mathworld.wolfram.com/LHospitalsRule.html

My book spells it as L'hospital, and so does Wolfram Alpha.

Wikipedia says, "In calculus, l'Hôpital's rule pronounced: [lopiˈtal] (also sometimes spelled l'Hospital's rule with silent "s" and identical pronunciation)"
 
Nice!
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Solving a Limit Problem using L'Hospital Rule
Replies
8
Views
1K
Evaluating a Limit with L'Hospital's Rule
Replies
6
Views
1K
Limit Calculation with L'Hospital's Rule: arctanx/arcsinx rigorously at x=0
Replies
5
Views
2K
Evaluating the Limit of Cosine Function Using L'Hospital's Rule - Explained
Replies
4
Views
2K
Limit as x approaches infinity.
Replies
2
Views
2K
How do you evaluate this limit?
Replies
8
Views
1K
Need help finding the limit of a function
Replies
5
Views
2K
L'Hospital's Rule and Integration
Replies
22
Views
4K
Limit of a Radical Expression without L'Hospital's Rule
Replies
11
Views
4K
Can l'Hospital's Rule be Used to Solve exp(i*k-a)*x=0 for x=inf?
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top