Limit Problem

  • #1
Prototype44
34
0

Homework Statement



lim f(x+h)-f(x)/h f(x)=(x+1)^(1/2) ans:1/2(x+1)^(1/2)
h→0

Homework Equations





The Attempt at a Solution


lim (x+h+1)^(1/2)-(x+1)^(1/2)/h lim (x+1)^(1/2)-(x+1)^(1/2)/h
h→0 h→0

Should the answer be D.N.E because the square roots cancel each other and leave 0/0
 
Last edited:

Answers and Replies

  • #2
SithsNGiggles
186
0
[itex]\lim_{h \to 0} \frac{\sqrt{x+h+1}-\sqrt{x+1}}{h}[/itex]

Have you tried multiplying the numerator and denominator by the conjugate of the numerator?
 
  • #3
36,194
8,180

Homework Statement



lim f(x+h)-f(x)/h f(x)=(x+1)^(1/2) ans:1/2(x+1)^(1/2)
h→0

Homework Equations





The Attempt at a Solution


lim (x+h+1)^(1/2)-(x+1)^(1/2)/h lim (x+1)^(1/2)-(x+1)^(1/2)/h
h→0 h→0

Should the answer be D.N.E because the square roots cancel each other and leave 0/0
No. This type of limit always is of the [0/0] indeterminate form.
 
  • #4
Prototype44
34
0
Figured it out
 

Suggested for: Limit Problem

  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
5
Views
851
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
0
Views
879
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
5
Views
927
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
5
Views
1K
Top