Riemann Sums and Area
The curve in red in the pictures below is
the graph of y = x2 + 1.
The goal is to approximate and then
compute exactly the area between the xaxis and the graph of y = x2 + 1 with x
between 0 and 2. The region being
described is shown

Riemann Sum Practice Problems
Questions:
1. Approximate the area under the curve
f ( x) = x 2 + 2,
2 x 1
with a Riemann sum, using six sub-intervals and right endpoints.
_
2 Approximate the area under the curve
f ( x) =
x + 1,
1 x 0
with a Riemann sum,

Implicit Differentiation and Related Rates
Implicit means implied or
understood though not
directly expressed
PART I: Implicit Differentiation
The equation
has an implicit meaning. It implicitly describes y as a function of x. The
equation can be made exp

EEE105
Lecture Notes
Chapter 9
Sinusoids and Phasors
Dr. Dahaman Ishak
[email protected]
Semester 1, 2014/2015
Overview
This chapter will cover alternating current.
A discussion of complex numbers is
included prior to introducing phasors.
Applications of