2.1 Tangent Lines and Finding Instantaneous Velocity
So I’m gonna rewrite my notes. Figured it was a good idea. Im hoping that Ill put the notes for all of my classes. I might also add my thoughts. Idk. We’ll see. This is my first Calculus lesson.
Secant Line: a line that passes through the curve at two points. In my class we called those points P and Q
Tangent Line: Line obtained by looking at the secant line as Q approaches P.
Slope of the tangent line = slope of curve at P
( I’ll try and add diagrams later)
Ex. Find slope of tangent to y= x² at x= 1/2
P (1/2, (1/2)² ) is a fixed point
Q is located at ( x, x²) where x approaches .5
From either side the mPQ is be 1 for this problem
.49 —> .5< — .51
mPQ denotes the slope of the secant line through points P and Q
Velocity
Suppose you drove 30 miles in 30 mins
What yo velocity? If it were a constant velocity it would be 60 miles per hour on average right? But what if velocity isnt constant?
You have to find find the tangent line.
Equation to find average velocity over an interval t to t +h :
s(t+h) — s(t) /h
- s = distance
- t= time
- h= difference between t and( t+h)
Slope of secant line ……
gives the average velocity of object over the integral. Seems I wrote so make that the last bit of notes wasn’t legible.
How are you guys handling note taking while also trying to her what your professor is saying? My teacher went somewhat fast but I think I did okay. Could do better though.
