March 12

Summary and Review of sections:
 

2.5.  Limits Involving Infinity

objective: to be able to determine infinite limits and limits at infinity graphically and algebraically

key ideas and/or vocabulary
infinite limits, vertical asymptotes, limits at infinity, horizontal asymptotes

• Infinite limits
•   definition on page 131
• vertical asymptotes definition on page 132
• Limits at Infinity
•   definition on page 134
• horizontal asymptotes definition on page 135
• Infinite Limits at Infinity

solved problems - using key ideas

• 
• verbal description of infinite limits, #1
• finding limits from a graph, #3
• Consider 
• finding infinite limits, #15,16
• Consider 
• important 

announcements
Homework.#2,4,8,18,20,32
 

2.6.  Tangents, Velocities and Other Rates of Change

objective: to be able to determine average rates of changes graphically, algebraically, and numerically
to be able to determine instantaneous rates of changes graphically, algebraically, and numerically
to be able to find the equation of the tangent to a function at a given point

key ideas and/or vocabulary

• secant lines, tangent lines, average rate of change, instantaneous rate of change, displacement functions,  average velocity, instantaneous velocity,  average rate of change of y with respect to x over an interval
• definition of tangent line page 143

Equation 2. 

• equation for secant line and tangent line given arbitrary points, #1
• find slope of tangent line by choosing two points on tangent line by taking limits
• find equation of the tangent line
• zoom in to see what appears to be a straight line
• using the definition of tangent and equation 2, #5
• finding equation of tangent line, #8

• position function - displacement
• average and instantaneous velocity 
• understanding the position function graphically, #13
• instantaneous velocity algebraically, #15.

• average rate of change of y with respect to x over an interval
• instantaneous rate of change = 
• estimating rates of change from data, #21

Classwork
Infinite Limits
 
 
 
 

QUESTION OF THE DAY

Find

SOLUTION

 

SOLUTION.