Why don't the secants cancel in this equation?

In summary, secants are used in this equation to represent a line intersecting a curve at two points, allowing us to find the slope of the curve at a specific point. The secants cannot cancel in this equation because they represent separate lines. If the secants are parallel, the equation simplifies to the slope of the line. Secants are necessary to accurately determine the slope at a specific point on a curve. The formula for calculating secants in this equation is (f(x+h)-f(x))/h, and it can be applied to any curve and any two points.
  • #1
bobsmith76
336
0

Homework Statement



Screenshot2012-01-25at35053AM.png


Homework Equations


The Attempt at a Solution



I don't see how they get from step one to two. I would think both secants would cancel since one is positive and the other is negative but that doesn't happen. i think i understand the manipulations of the tangents but not entirely
 
Physics news on Phys.org
  • #2
its simple. just expand the numerator and then take sec x common
 
  • #3
ok, I get it

ab - ac = a(b-c)
 

1. Why are secants used in this equation?

Secants are used in this equation because they represent a line that intersects a curve at two points. This is important because it helps us find the slope of a curve at a specific point, which is useful in many scientific applications.

2. Can the secants ever cancel in this equation?

No, the secants cannot cancel in this equation because they represent two different lines that are intersecting at different points. Even if the points are close together, the lines are still separate and cannot be combined or eliminated.

3. What happens if the secants are parallel in this equation?

If the secants are parallel, it means that the curve is a straight line and the slope at every point on the line is the same. In this case, the equation will simplify to the slope of the line and the secants will not cancel.

4. Why do we need to use secants instead of just finding the slope from two points?

Using secants allows us to find the slope of a curve at a specific point, rather than just between two points. This is important because the slope of a curve can change at different points, and using secants helps us to accurately determine the slope at a specific point.

5. Is there a specific formula for calculating secants in this equation?

Yes, the formula for calculating secants in this equation is (f(x+h)-f(x))/h, where f(x) represents the curve and h represents the distance between the two points where the secants intersect the curve. This formula can be applied to any curve and any two points to find the slope at a specific point on the curve.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
3
Views
2K
  • Precalculus Mathematics Homework Help
Replies
7
Views
2K
  • Precalculus Mathematics Homework Help
Replies
25
Views
327
  • Calculus and Beyond Homework Help
Replies
2
Views
2K
  • Precalculus Mathematics Homework Help
Replies
7
Views
6K
Replies
8
Views
2K
  • Calculus and Beyond Homework Help
Replies
19
Views
5K
  • Precalculus Mathematics Homework Help
Replies
2
Views
2K
  • Precalculus Mathematics Homework Help
Replies
7
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
Back
Top