Multivariable sketch

  • Thread starter seiferseph
  • Start date
  • #1
102
0
Here is the problem i'm having some trouble with. The answer is fairly simple, it is the power of the e function. (the parabola x = y^2 + 1) i'm not sure how to get that, i could use some hints/help, thanks!
1f4ff688.jpg
 

Answers and Replies

  • #2
StatusX
Homework Helper
2,564
1
Think about what values for the power of an exponent give a result greater than one.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,833
964
Are you aware that "The answer is fairly simple, it is the power of the e function. (the parabola x = y^2 + 1)" is NOT precisely true? That is, the region you are asked to sketch is NOT the parabola itself. The parabola is a boundary of the region. Indeed if you think about the fact that "power of the e function" is NOT x= y^2+ 1 nor a parabola, you might see what StatusX means!
 
  • #4
benorin
Homework Helper
Insights Author
Gold Member
1,307
108
I'll be kind: recall that [tex]e^w \geq 1[/tex] if, and only if, [tex]w\geq 0,[/tex] that is, if, and only if the exponent of e is greater than or equal to 0. You are asked to find (and sketch) all points in xy-plane (e.g. all values of x and y) such that [tex]e^{1-x+y^{2}}\geq 1,[/tex] which occurs if, and only if, [tex]1-x+y^{2}\geq 0[/tex] which describes the region in the xy-plane bounded by (and to the left of) the parabola [tex]x=1+y^{2}[/tex].
 
  • #5
102
0
benorin said:
I'll be kind: recall that [tex]e^w \geq 1[/tex] if, and only if, [tex]w\geq 0,[/tex] that is, if, and only if the exponent of e is greater than or equal to 0. You are asked to find (and sketch) all points in xy-plane (e.g. all values of x and y) such that [tex]e^{1-x+y^{2}}\geq 1,[/tex] which occurs if, and only if, [tex]1-x+y^{2}\geq 0[/tex] which describes the region in the xy-plane bounded by (and to the left of) the parabola [tex]x=1+y^{2}[/tex].

ohh, i see, i forgot that to get thats how to get the entire function greater than 1, i get it now, thanks everyone!
 

Related Threads on Multivariable sketch

Replies
6
Views
416
Replies
3
Views
1K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
10
Views
5K
  • Last Post
Replies
6
Views
5K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
3
Views
1K
Top