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

Squeeze theorem

Intermediate value theorema
Basically, memorize everything.
LESSER SALIENT POINTS
CHAPTER 1
nullptr
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=(2x8)/(x4) 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/(x1)) 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

MEMORIZE FORMULAS

Product rule is IMPORTANT!

L'HOPITALS RULE IS ALSO IMPORTANT!!!

Chain rule too

Trig

You can only take scalars out of a limit, not variables.