MOST SALIENT POINTS

Limit Laws
- As long as it exists and it makes sense in basic arithmetic, it would work
Product Rule
L'Hopital's Rule
- ONLY FOR L'HOPITAL, KANG HAO WANTS US TO WRITE "USING L'HOPITAL'S RULE", OTHERWISE DEDUCTION OF MARKS IS PROBABLE
Chain Rule
Trig stuff

Basically, memorize everything.

LESSER SALIENT POINTS

CHAPTER 1

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CHAPTER 2

Vertical asymptotes do not have to have an existing limit as the limits from both sides do not need to match up.
- To find one, set denominator to 0.
Squeeze Theoreom (bound it by a range)
Polynomial, Rational (except for when the denominator is 0) and sinx, cos, tanx (except for odd multiples of pi/2) are continuous but need to state.
Limit Laws (such as addition of two limits) ONLY APPLY WHEN INDIVIDUAL LIMITS EXIST
y=(2x-8)/(x-4) AND y=2 are NOT the same (check when x=4) Can do for limits since most limits go towards 4 and when it doesnt, it's away from the problem point and it doesn't matter.
As long as you can plug in or cancel out, no need to do left and right limits
With absolute values in either numerator or denominator, do both left and right limits
for i and j for vectors in limits, do them separately
Intermediate value theorem steps
- Plug in the boundary points into the function
- If one is negative and the other is positive, there is a 0 result in between. Therefore it passes through there, therefore this is a root
- ALSO THE EQUATION HAS TO BE CONTINUOUS
Essential discontinuity only works when x->0 (sin(anything/x))
- If sin(1/(x-1)) the essential discontinuity is when x->1.
- for x(sin(PI/x)) when x->0, -abs(x)<=x(sin(PI/x))<=abs(x) (less than or equal to; this is important!)

CHAPTER 3