Le^x-(1+x/1!+x^2/2!)l <= e/6 for all x E [0,1].

  • Thread starter squenshl
  • Start date
  • #1
squenshl
479
4
I have a problem.
How do I show that le^x-(1+x/1!+x^2/2!)l <= e/6 for all x E [0,1].
 

Answers and Replies

  • #2
Phrak
4,265
6


Show that the equation is true at the boundries. Show that the term on the left is monotonic in x (if, indeed, it is).
 
  • #3
adriank
534
1


What a strange coincidence. I saw this thread only after posting my example in this thread.

If you don't want to see the full solution, here's a hint: Taylor's theorem.
 
  • #4
ice109
1,714
6


how to show that a function is monotonic increasing? show that f(x+1) >= f(x) for all x?
 
  • #5
dx
Homework Helper
Gold Member
2,119
41


how to show that a function is monotonic increasing? show that f(x+1) >= f(x) for all x?

No, that won't work. A function is monotonic increasing if f(x) ≥ f(y) whenever x ≥ y.
 

Suggested for: Le^x-(1+x/1!+x^2/2!)l <= e/6 for all x E [0,1].

Replies
24
Views
1K
Replies
2
Views
689
  • Last Post
Replies
1
Views
387
  • Last Post
Replies
6
Views
703
  • Last Post
Replies
3
Views
595
Replies
8
Views
877
  • Last Post
Replies
4
Views
563
Replies
3
Views
715
Replies
1
Views
659
Replies
11
Views
764
Top