Math 115 MWF

Math 115 Enhanced MTWRF

Monday, Section 4.3

 

Introduce the concept of vertical and horizontal asymptotes from calculus perspective and relate it to Precalculus background.

 

Problems 1: Find asymptotes for a rational function.

 

Review how to sketch functions incorporating asymptotes.

 

Problem 2: Sketch a polynomial function.

 

Problem 3: Sketch a rational function.

 

HW for Wednesday:

4.3: #2, 4, 8, 10, 16, 24, 28, 30, 38

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Wednesday, Section 4.3

 

Review the concepts introduced on Monday.

 

Problem 4: Sketch a given rational function with two vertical asymptotes and a horizontal asymptote.

 

Problem 5: Sketch a function without explicitly knowing f(x), just using information about the intercepts, key points, definitions of asymptotes, and sign charts for the first and second derivative.

 

HW for Friday:

4.3: 48,54,58,62,64,67,70

Monday, Section 4.3

 

Introduce the concept of vertical and horizontal asymptotes from calculus perspective and relate it to Precalculus background.

 

Problems 1: Find asymptotes for a rational function.

 

Review how to sketch functions incorporating asymptotes.

 

Problem 2: Sketch a polynomial function.

 

Problem 3: Sketch a rational function.

 

HW for Wednesday:

4.3: #2, 4, 8, 10, 16, 24, 28, 30, 38

 

Tuesday, Section 4.3

 

Problem 4: Sketch a given rational function with two vertical asymptotes and a horizontal asymtote.

 

Problem 5: Sketch a function without explicitly knowing f(x), just using information about the intercepts, key points, definitions of asymptotes, and sign charts for the first and second derivative.

 

Group Work 6: Have the class work in groups of three and sketch a function without explicitly knowing f(x), just using information about the intercepts, key points, definitions of asymptotes, and sign charts for the first and second derivative.

 

HW for Wednesday:

4.3: 48,54,56,58,62,64,67,70

 

Group Study after class for 1 hour.

 

 

Wednesday, Section 4.4

 

Introduce the concepts of absolute extreme. Examine graphs and determine absolute extrema.

 

Discuss when we have absolute extrema on a closed domain and how to find these values.

 

Problem 7: Find absolute extrema for a continuous polynomial on a closed domain with at least one critical point outside the domain.

 

Problem 8: Find absolute extrema for a function with an open domain.

 

Group work 9: Have students find absolute extrema for a rational function that is continuous on a specified closed domain.

 

HW for Thursday:

4.4: #4,6,8,10,12,14,16,26,29

 

Group Study after class for 1 hour.

 

Thursday, Section 4.4

 

Problem 10 & 11: Two applications and word problems on finding absolute extrema.

 

Group work 12 & 13: Two application problems to find absolute extrema.

 

HW for Friday:

Chapter 4 Review: #2,3,4,10,16,22

Study for Friday's quiz on curve sketching.

 

Group Study after class for 1 hour.