Limits and continuity

Learning tasks

A) Limit at a point: definitions
1) Computing limits from the definition	Ex 1 Ex 2 Ex 3 Ex 4
B) Limit at a point: foundational properties
2) Using local boundedness and uniqueness	Ex 5 Ex 6 Ex 7 Ex 8
C) Sequential characterization (Heine)
3) Disproving limits by the two-sequence test	Ex 9 Ex 10 Ex 11
D) Operations on limits
4) Computing limits by algebraic operations	Ex 12 Ex 13 Ex 14 Ex 15 Ex 16 Ex 17
5) Lifting indeterminate forms	Ex 18 Ex 19 Ex 20 Ex 21
E) Continuity at a point
6) Establishing continuity at a point	Ex 22 Ex 23 Ex 24 Ex 25 Ex 26 Ex 27
7) Constructing continuous extensions	Ex 28 Ex 29 Ex 30
F) Continuity on an interval\(\virgule\) TVI\(\virgule\) image of an interval
8) Proving existence via TVI	Ex 31 Ex 32 Ex 33 Ex 34
9) Locating roots of polynomial and transcendental equations	Ex 35 Ex 36 Ex 37 Ex 38 Ex 39
G) Continuous functions on a segment
10) Applying the bornes-atteintes theorem	Ex 40 Ex 41 Ex 42
11) Using the continuous monotone bijection theorem	Ex 43 Ex 44 Ex 45
H) Complex-valued functions of a real variable
12) Computing limits and continuity of complex-valued real-variable functions	Ex 46 Ex 47 Ex 48

Lesson
Text book

Exercises Correction
A) Limit at a point: definitions
    1) Computing limits from the definition Ex 1 Ex 2 Ex 3 Ex 4
B) Limit at a point: foundational properties
    2) Using local boundedness and uniqueness Ex 5 Ex 6 Ex 7 Ex 8
C) Sequential characterization (Heine)
    3) Disproving limits by the two-sequence test Ex 9 Ex 10 Ex 11
D) Operations on limits
    4) Computing limits by algebraic operations Ex 12 Ex 13 Ex 14 Ex 15 Ex 16 Ex 17
    5) Lifting indeterminate forms Ex 18 Ex 19 Ex 20 Ex 21
E) Continuity at a point
    6) Establishing continuity at a point Ex 22 Ex 23 Ex 24 Ex 25 Ex 26 Ex 27
    7) Constructing continuous extensions Ex 28 Ex 29 Ex 30
F) Continuity on an interval\(\virgule\) TVI\(\virgule\) image of an interval
    8) Proving existence via TVI Ex 31 Ex 32 Ex 33 Ex 34
    9) Locating roots of polynomial and transcendental equations Ex 35 Ex 36 Ex 37 Ex 38 Ex 39
G) Continuous functions on a segment
    10) Applying the bornes-atteintes theorem Ex 40 Ex 41 Ex 42
    11) Using the continuous monotone bijection theorem Ex 43 Ex 44 Ex 45
H) Complex-valued functions of a real variable
    12) Computing limits and continuity of complex-valued real-variable functions Ex 46 Ex 47 Ex 48

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