Reading Assignments -
Math 101 - Calculus I
October 1997
Be sure to check back often, because the assignments may change.
For October 1
Exam 1 today. No Reading Assignment.
For October 3
Section 2.5 Average and Instantaneous Rates: Defining the Derivative
- To read: All. Be warned: This is a hard section!
- Be sure to understand: Example 1,
the Section on page 143 Average Speeds, Instantaneous Speeds, and Limits, and the formal definition of the derivative
Email Subject Line: Math 101 10/3 Your Name
Reading Questions:
- Let f(x)=x^{2}. Find the slope of the secant line from x=-2 to x=4.
- For a function f, what does the difference quotient
( f(a+h) - f(a) )/ h measure?
- Let f(x)=x^{2}. What is the average rate of change of f
from x=1 to x=3?
For October 6
Section 2.6 Limits and Continuity
- To read: All, but you may skip the formal definition of the limit on page 155.
- Be sure to understand:
The connection between Examples 2 and 3; the definition of continuity
on page 157
Email Subject Line: Math 101 10/6 Your Name
Reading Questions:
- Let g(x)=(x^{2} - 9)/(x-3) as in Example 2.
- Is g(x) defined at x=3? Why or why not?
- What is lim_{x->3} g(x) ? Why?
- Is n(x) in Example 8 continuous at x= -3? Why or why not?
For October 8
Section 2.7 Limits Involving Infinity; New Limits from Old
- To read:
All, but you may skip Examples 4, 5, 7 and the Squeeze Principle
- Be sure to understand:
Examples 1 and 3; the section
Finding Limis Graphically and Numerically
Email Subject Line: Math 101 10/8 Your Name
Reading Questions:
Find the following limits: Explain your answers.
- lim_{x->infinity} 1/x^{3}
- lim_{x->0+} 1/x^{3}
- lim_{x->infinity} cos(x)
For October 10
Section 3.1 Derivatives of Power Functions and Polynomials
- To read:
All except for the Optional Section on pages 190-191
- Be sure to understand:
Examples 1 and 2; Theorems 1, 2, and 3; the definition of an antiderivative
Section 3.2 Using Derivative and Antiderivative Formulas
- To read:
The section Modeling Motion: Acceleration, Velocity, and Positions
plus Example 4 from Section 2.1
- Be sure to understand:
Example 2
Email Subject Line: Math 101 10/10 Your Name
Reading Questions:
- Let f(x)=x^{2}. What is f'(x)?
- What does it mean for the function F to be an antiderivative of the function f?
- The equation h(t)=-16t^{2} + v_{0} t + h_{0} gives the height of a falling object at time t. What do the constants v_{0} and h_{0} measure?
For October 15
Section 3.3 Derivatives of Exponential and Logarithm Functions
- To read:
All, but you may skip the section on Calculating the Derivative of b^{x}. We'll discuss this in class.
- Be sure to understand:
Theorems 5, 6, and 7
Email Subject Line: Math 101 10/15 Your Name
Reading Questions:
Since this is the first day after Fall Break, you don't have to send these in, but you should think about them.
- Find an antiderivative for f(x)=e^{x}.
- What is the derivative of g(x)=ln(x).
- What is the slope of the line tangent to y=e^{x} at the point (0,1)?
For October 17
Section 3.4 Derivatives of Trigonometric Functions
- To read:
All, but you may skim the subsection "Differentiating the Sine Function"
(we'll talk about this in more detail in class) and you may skip page 213.
- Be sure to understand:
Examples 1 and 2
Email Subject Line: Math 101 10/17 Your Name
Reading Questions:
- What is lim_{h->0} ( cos(h) - 1) / h?
- What is lim_{h->0} sin(h) / h?
- Let f(x)=sin(x) + cos(x). What is f'(x)?
For October 20
Section 3.5 New Derivatives from Old: The Product and Quotient Rules
- To read:
All
- Be sure to understand:
Theorems 9 and 10, and Exhibit B, pg 219
Email Subject Line: Math 101 10/20 Your Name
Reading Questions:
Find the derivatives of the following functions. Be sure to justify your answer.
- f(x) = x sin(x)
- g(x) = x / sin(x)
- h(x) = x ln(x) - x
For October 22
Exam 2 today. No Reading Assignment.
For October 24
Section 3.6 New Derivatives from Old: The Chain Rule
- To read:
All
- Be sure to understand:
Theorem 11 and Example 3
Email Subject Line: Math 101 10/24 Your Name
Reading Questions:
Find the derivatives of the following functions:
- f(x) = sin(x^{3})
- g(x) = ( sin(x) )^{3}
- h(x) = e^{2x}
For October 26
Reread Section 3.6.
No Reading Questions to email today.
For October 29
Differentiation Exam today. No reading assignment.
For October 31
Section 4.1 Differential Equations and Their Solutions
- To read: Reread this section for Friday.
- Be sure to understand:
Examples 3 and 6.
Email Subject Line: Math 101 10/31 Your Name
Reading Questions:
Decide whether the function y(t) is a solution to the differential equation.
- y(t)=sin(t); -y=y''
- y(t)=e^{2t}; y=y'
- y(t)=(1/2)e^{t2}; y'=ty
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