MOST SALIENT POINTS
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Limit Laws
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As long as it exists and it makes sense in basic arithmetic, it would work
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Product Rule
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L'Hopital's Rule
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ONLY FOR L'HOPITAL, KANG HAO WANTS US TO WRITE "USING L'HOPITAL'S RULE", OTHERWISE DEDUCTION OF MARKS IS PROBABLE
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Chain Rule
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Trig stuff
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Squeeze theorem
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Intermediate value theorema
Basically, memorize everything.
LESSER SALIENT POINTS
CHAPTER 1
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CHAPTER 2
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Vertical asymptotes do not have to have an existing limit as the limits from both sides do not need to match up.
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To find one, set denominator to 0.
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Squeeze Theoreom (bound it by a range)
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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.
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Limit Laws (such as addition of two limits) ONLY APPLY WHEN INDIVIDUAL LIMITS EXIST
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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.
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As long as you can plug in or cancel out, no need to do left and right limits
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With absolute values in either numerator or denominator, do both left and right limits
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for i and j for vectors in limits, do them separately
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Intermediate value theorem steps
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Plug in the boundary points into the function
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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
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ALSO THE EQUATION HAS TO BE CONTINUOUS
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Essential discontinuity only works when x->0 (sin(anything/x))
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If sin(1/(x-1)) the essential discontinuity is when x->1.
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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
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MEMORIZE FORMULAS
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Product rule is IMPORTANT!
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L'HOPITALS RULE IS ALSO IMPORTANT!!!
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Chain rule too
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Trig
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You can only take scalars out of a limit, not variables.