Evaluate limit

  • Thread starter Aviegaille
  • Start date
  • #1

Homework Statement


Evaluate lim h->0 ((8+h)^⅓ -2)/h.


Homework Equations


Hint: Let 8+h=x^3


The Attempt at a Solution


I've uploaded a picture of my calculation. But I am not sure if that is the final answer or is there a following step to get the answer.
 

Attachments

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
619
Why do you think that as h->0 with x^3=8+h that x->(-3)? And why do you think that (x^3)^(1/3)=x^3?
 
  • #3
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728

Homework Statement


Evaluate lim h->0 ((8+h)^⅓ -2)/h.


Homework Equations


Hint: Let 8+h=x^3


The Attempt at a Solution


I've uploaded a picture of my calculation. But I am not sure if that is the final answer or is there a following step to get the answer.
Please do not post thumbnails; they cannot be viewed on some media! Just type out things directly.
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,833
956
I don't know exactly which of many possible methods you are expected to use here, but did you notice that this limit is precisely that defining the derivative of f(x) at x= 8, with [itex]f(x)= x^{2/3}[/itex]?
 

Related Threads on Evaluate limit

  • Last Post
Replies
12
Views
952
  • Last Post
Replies
13
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
5
Views
5K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
17
Views
2K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
1
Views
4K
Top