INVERTIBLE FUNCTIONS 1. In each case, explain or verify that the given function is invertible. Find the inverse function.
A.
m f ( m)
1 2 3 4 5 0.09 2.10 5.60 7.80 9.40
B.
S (t ) = At 3 + K where A and K are constants.
C.
5
G(x)
0 0 10
x
2. The life expec
WORKSHEET 2 - Fall 1995 1. For each graph below of a function f (x), sketch a graph of its derivative f (x): a) b) c)
d)
e)
f)
g)
h)
i)
2. Without using the concept of a limit (and thus derivative), write the equations of all lines through the point (a, a
Calculus and Vectors How to get an A+
6.7 Operations with Algebraic Vectors in R3 A 3D Algebraic Vectors A 3D Algebraic Vector may be written in components form as: r v = (v x , v y , v z ) or in terms of unit vectors as: r r r r v = vxi + v y j + vz k an
Calculus and Vectors How to get an A+
6.6 Operations with Algebraic Vectors in R2 A 2D Algebraic Vectors A 2D Algebraic Vector may be written in components form as: r v = (v x , v y ) or in terms of unit vectors as: r r r v = vxi + v y j and has a magnitu
Calculus and Vectors How to get an A+
6.5 Vectors in R2 and R3 A Polar Coordinates Given a Cartesian system of coordinates, a 2D r r vector v may be defined by its magnitude | v | and the counter-clockwise angle between the positive direction of the x-axi
Calculus and Vectors How to get an A+
6.4 Properties of Vectors A Properties of Vectors rrrr a +b =b +a rrrrr a +0 = 0+a = a r r r rr a + (a ) = (a ) + a = 0 rr rr rr (a + b ) + c = a + (b + c ) r r | ka |=| k | | a | r r r r k (a + b ) = ka + kb r r r (k
Calculus and Vectors How to get an A+
6.3 Multiplication of a Vector by a Scalar B Properties A Multiplication of a Vector by a Scalar r By multiplying a vector v by a scalar k we obtain The following properties apply for multiplication of a vector r a ne