Problem Calculus

292 views

Published on

Published in: Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
292
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
4
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Problem Calculus

  1. 1. Problem 50Find the shortest distance from the point (4, 2) to the ellipse x2 + 3y2 = 12.Solution:Click here to show or hide the solutionfromBy trial and error
  2. 2. The nearest point is (3, 1)Nearest distance: answer → slope of tangent at any pointThus, slope of normal at any point isEquation of normal: the same equation as above (okay)Problem 51Find the shortest distance from the point (1 + n, 0) to the curve y = xn, n > 0.Solution:Click here to show or hide the solution
  3. 3. by inspection: x = 1 1 raise to any positive number is 1 answer slope of tangent at any pointThus, slope of normal at any point isEquation of normal:By trial and error
  4. 4. Nearest point on the curve is (3, 3)Shortest distance answer

×