PPT-Rectilinear Motion and Tangent Lines

Alyssa Cobranchi AP Calculus Rectilinear Motion Introduction Rectilinear Motion is the movement of a particle on a straight line It is an application of the derivative of a function Some examples can include a race car moving along a straight track an object thrown from the top of a building and falling straight down or a ball thrown straight up and then falling straight down. Notation dx dx y 00 f 00 Thus dx dx dy dx Example Find the second derivatives of the following functions a 2 x y 00 2 b y 00 c 5 4 5 y 00 The 64257rst derivative gives information about whether a funct ion increases or decreases In fact A d Experiences from Avalanche Studios. Emil Persson. Senior Graphics Programmer. @_Humus_. Just how big is Just Cause 2?. Unit is meters. [-16384 .. 16384]. 32km x 32km. 1024 km. 2. 400 mi. 2. Issues. Sections 4.2 and 4.3. Updates & Reminders. The date and time of the final: Thursday, December 11 from 10 a.m. to 12 p.m. MLT 208. . There is no lab this week.. Test #1 will take place on Thursday, 9/18.. Recitation . 3. Distance Measures. Rectilinear distance (L. 1. norm). d(X, P. i. ) = |x - a. i. | + |y - b. i. |. Straight line or Euclidean distance (L. 2. norm). d(X, P. i. ) =. Tchebyshev distance (L. Tangent Lines. Average Rate of Change. The . average rate of change. of a quantity over a period of time is the slope on that interval of time.. Ex.:. . Find the average rate of change of . f(x) = x. Theorem:. . Two chords are congruent IFF they are equidistant from the center.. . A. B. C. D. M. L. P. AD .  BC. IFF. LP .  PM. Ex. 1: . IN . A, PR = 2x + 5 . and QR = 3x –27. Find x.. P. Properties of Tangents. Geometry Honors. What and Why. What?. Find the relationship between a radius and a tangent, and between two tangents drawn from the same point.. Circumscribe a circle. Why?. To use tangents to circles in real-world situations, such as working in a machine shop.. Slope is the rate of change . or. . . Secant slope. the slope between two points. . tangent slope. the slope at one point of contact. and is based upon a limit.. Noun: derivative. Verb: differentiation or to. A brief journey into Section . 4.5a. Analysis of the Tangent Function. by. Domain: All . reals. except odd. multiples of. Range:. Continuous on its domain. Increasing on each interval in. i. ts domain. Session 5. The Derivative. Integrals . Review. Plot a graph of the function f(x), where f represents how something is changing (e.g. it might be speed or acceleration). We write something like f(x) = x. Math 200. Goals. Be able to compute an equation of the tangent plane at a point on the surface z = f(x,y).. Given an implicitly defined level surface F(x,y,z) = k, be able to compute an equation of the tangent plane at a point on the surface.. the . process of moving . or . changing . places . or position. Anything you do while moving is motion.. Fact: Speed is a major type of Motion. Determining motion. In order to determine motion you must know direction and speed. Write the 3 steps to determine if a function is continuous . 1. ) F . is defined at c; that is, c is in the domain of f so that f(c) equals a #.. 2) . 3) . *So the same output is approached from both sides. . i.e. . they do not meet).. What is the shortest distance between them?.  .  .  .  . Also find the co-ordinates of . and . ..  . shortest distance. must be perpendicular to both lines.. Let . Then .