Function, Limit, and Continuity
Some Trigonometric Identities
tan A = cos
sin2 A + cos2 A = 1
A real-life example:
the horizontal displacement of the piston in the
below reciprocating mechanism is a function of
To Find the Arc Length of a
VECTORS ON A PLANE
We denote the directed line segment extending from the
point P (the initial point) to the point Q (the terminal
The length of a vector is its magnitude, denoted
We use the term vector to
THE CROSS PRODUCT
For two vectors a = a1, a2, a3 and b = b1, b2, b3 in V3,
we define the cross product (or vector product) of a
and b to be
The order is important!
While weve used the determinant notation, this is not
really a dete
Given a function, f , wed like to find another function F
such that F(x) = f (x).
We call such a function F an antiderivative of f.
Finding Several Antiderivatives of a Given Function
Secant Lines and Tangent Lines
Consider the curve y = x2 + 1.
A secant line is a line between a
pair of points on the curve.
The secant line shown here has a
And the secant line has the
If s(t) represents the position of an object relative to
some fixed location at time t as the object moves along
a straight line, then the instantaneous velocity at time
t = a is given by