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

Limit of [x^2(3 + sinx)] / [(x + sinx)^2]

  • Thread starter PhizKid
  • Start date
  • #1
475
1

Homework Statement


8TmfF.png



Homework Equations





The Attempt at a Solution



I expanded everything out and got [3x^2 + x^2*sin(x)] / [x^2 + 2sin(x) + sin^2(x)] and I tried splitting the problem but it didn't work because the denominator is always 0 when I try plugging in '0' for 'x.' I can't find any way to cancel out the denominator
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
You can't really 'cancel out' the denominator. You could try l'Hopital's rule or substituting a series expansion of sin(x). Or factoring x^2 out of the denominator and using a known limit like sin(x)/x.
 
  • #3
475
1
Oops, sorry, I forgot to mention this is for an introductory Calc 1 course, so none of that l'Hopital stuff...

But what do you mean about substituting a series expansion?
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
Oops, sorry, I forgot to mention this is for an introductory Calc 1 course, so none of that l'Hopital stuff...

But what do you mean about substituting a series expansion?
I think my last suggestion about factoring x^2 out of the denominator is the best. I added that to my post in an edit. Try that.
 
  • #5
475
1
So then I get:

[x^2(3 + sinx)] / [x^2(1 + 2sinx/x + sin^2x/x] and cancel out the x^2's:

(3 + sinx) / (1 + 2sinx/x + sin^2x/x)

Editl: Oh, I had made an algebra error. I got it now, thanks
 

Related Threads for: Limit of [x^2(3 + sinx)] / [(x + sinx)^2]

Replies
5
Views
57K
  • Last Post
Replies
5
Views
13K
  • Last Post
Replies
7
Views
2K
Replies
6
Views
5K
  • Last Post
Replies
21
Views
10K
  • Last Post
Replies
5
Views
3K
Replies
8
Views
9K
Replies
8
Views
8K
Top