1. 2.1 - The Tangent and Velocity Problems
Calculus = The branch of mathematics dealing with change and motion / and quantites that approach other quantites…
2 Branches of Calculus
Differential --> The Tangent & Velocity Problems
Integral --> The Area Problem
Key Idea: Limits
Key people:
Isaac Newton
Gottfried Leibniz

2. The Tangent and Velocity Problems
Explanation…
ex: Find the equation of the tangent line to the parabola y = x2 at the point (1, 1).

4. Tabular Functions
ex: Use the data to draw the graph of this function and estimate the slope of the tangent line at the point where t = 0.04
100 90 80 70 60 50
0.02
0.04
0.06
0.08 P

5. Pick table values on either side of tangent point…
Triangle Method
(x1, y1)
(x2, y2) P x y

6. The Velocity Problem
ex: A ball is dropped from an observation tower 450m above the ground. The ball drops according to position equation:
Find the velocity of the ball after 5 seconds.
Average Velocity =
Distance Traveled
Time Elapsed

7. Distance traveled =
Time elapsed = = 0.1 sec
Average Velocity for t= [5 to 5.1] = m/s
We can continue to make the interval smaller and smaller and compute the average velocity…
It appears we are reaching a limiting value… thus the instantaneous velocity after 5s = 49 m/s

8. The Velocity Problem
s (position)
t (time) t1 t2

9. SHOULDA TAKEN STATS!!
HW 2.1
pg 100
#’s 1-8 all
MATH MELTDOWN!!!