Unit Vector Problem

1. The problem statement, all variables and given/known data



For the equations:



y1 = 1-x^2



y2 = x^2 -1



find the unit tangent vectors to each curve at their point of intersection.



2. Relevant equations



d/dx (y1) = -2x



d/dx (y2) = 2x





3. The attempt at a solution



After solving for points of intersection between the two equations (-1,0) & (1, 0), I proceeded to ask the derivative for the slope of these points.



The slope at x = 1:

for y1 = -2j



for y2 = 2j





The slope at x = -1:

for y1 = 2j



for y2 = -2j



Next, I divided each resultant vector by the magnitude, (2), to obtain the unit vector.



However, this appears to be incorrect, and I am not sure why.



Attached is a photo:

Attached Images

Cal Hw 11.3.jpg (80.3 KB)