• Support PF! Buy your school textbooks, materials and every day products Here!

Limit Problem

  • #1

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
[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
33,503
5,191

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
Figured it out
 

Related Threads on Limit Problem

  • Last Post
Replies
5
Views
962
  • Last Post
Replies
4
Views
775
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
3
Views
620
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
14
Views
1K
  • Last Post
Replies
16
Views
2K
  • Last Post
Replies
8
Views
703
  • Last Post
Replies
4
Views
700
Top