Worked on homework as most students were out for senior retreat.
Wednesday
Assessment on limits graphically and algebraically. Examined how to make a limit exist by tinkering with the value of a constant, allowing a trinomial to factor. Looked at function dominance. Exponentials (bigger bases win out) are stronger than polynomials (bigger exponents win out) are stronger than logarithmic functions. Limits where the x approaches infinity are just horizontal asymptote questions, where the precalc rules comparing numerator and denominator apply (and should make sense, based on domination principle). We will look more at limits that yield infinity (better known as Vertical Asymptotes) on Friday. Lecture notes
Homework: (Due by end of class Friday)
p. 88: 4, 25, 26, 33-45 (multiples of 3)
p. 202: 13-22
(F-LF1)
(F-BF2)
Resources:
Section 1.5: (infinite limits; limits that yield infinity)
long but good video: https://www.youtube.com/watch?v=-vwcLvb9A0s
very basics of the concepts: https://www.youtube.com/watch?v=a2Ia_ZlUCaQ
first half of this video deals with section 1.5; second half deals with section 3.5: https://www.youtube.com/watch?v=tFHALKP22ao
Section 3.5 (limits at infinity) https://www.youtube.com/watch?v=FVJNuukADeQ
also keep in mind the function dominance hierarchy. an exponential function will outgrow a polynomial function.
more examples: https://www.youtube.com/watch?v=KcqO1fX9b_I
Prefer to read? these links are awesome:
overview: http://tutorial.math.lamar.edu/Classes/CalcI/InfiniteLimits.aspx
in depth part 1: http://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityI.aspx
exponentials/logs/trigs: http://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityII.aspx
No journal because of intermezzo schedule. Passed back first assessment. Retakes begin Monday in DS. Continued to discuss limits at infinity (Horizontal asymptotes) and limits that produce infinity (vertical asymptotes). Looked at definitions for both and method of using 0+ and 0- to determine limits when direct sub and cancellation and rationalization fail or cannot be used. Lecture notes
Homework: Read section 1.4 for Monday
turned in p. 88 and 202 if finished; can turn in Monday if needed. See above resources for help.