## 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

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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

• 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.