MHB What is the limit of a complex fraction with L'Hopital's rule?

  • Thread starter Thread starter karush
  • Start date Start date
Click For Summary
The limit of the complex fraction as x approaches 2 results in an indeterminate form of 0/0, prompting the use of L'Hôpital's rule or the conjugate method for evaluation. Participants discuss the effectiveness of L'Hôpital's rule in resolving the limit, while also considering the conjugate multiplication approach. Both methods are viable, with L'Hôpital's rule being favored for its straightforward application. The discussion emphasizes the importance of recognizing indeterminate forms and selecting appropriate techniques for limit evaluation. Ultimately, the limit can be resolved effectively using either method.
karush
Gold Member
MHB
Messages
3,240
Reaction score
5
\tiny{s8.1.6.64}
Evaluate
$\displaystyle\lim_{x \to 2}
\dfrac{\sqrt{6-x}{-2}}{\sqrt{3-x}-1}$

ok so if you plug in 2 directly you get $\dfrac{0}{0}$

So we either use L'H rule or use conjugate

or is there better way
 
Physics news on Phys.org
L'Hopital works

you can also multiply numerator and denominator by both conjugates
 
Last edited by a moderator:
Thread 'Problem with calculating projections of curl using rotation of contour'

Thread 'Problem with calculating projections of curl using rotation of contour'

Hello! I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem. Given: ##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0## ##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1## ##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0## I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
View full post »

Similar threads

MHB 1.6.1 AP Calculus Exam Limits with L'H
  • · Replies 3 ·
Replies
3
Views
2K
MHB Can this project revolutionize surfing?
  • · Replies 8 ·
Replies
8
Views
1K
MHB 7.1.17 int e^{-\dfrac{x^2}{2}} dx from 0 to infty
  • · Replies 3 ·
Replies
3
Views
2K
MHB 1.4.203 AP calculus practice question on Limits
  • · Replies 1 ·
Replies
1
Views
2K
MHB 5.5.2 average value of sqrt{x} [0,4]
  • · Replies 1 ·
Replies
1
Views
2K
MHB Limit $\frac{f(x)}{g(x)}$: Solve w/ L'H Rule
  • · Replies 4 ·
Replies
4
Views
2K
MHB -6.r.10 evaluate int with u v subst
  • · Replies 2 ·
Replies
2
Views
900
MHB Find Limit of $\displaystyle\frac{\sec x +3}{7x-\tan y}$ at (0,$\dfrac{\pi}{4}$)
  • · Replies 3 ·
Replies
3
Views
1K
MHB 1.3 find dx of (7+9x-6\sqrt{x})/x
  • · Replies 4 ·
Replies
4
Views
1K
MHB 2.1.207 AP calculus practice exam problem Lim with tan(4X)/6x
  • · Replies 2 ·
Replies
2
Views
2K