# MATH 1LS3 Study Guide - Midterm Guide: Integral, Inflection Point, Inflection

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12 Aug 2016
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Midterm 1 22:44
Intervals of Inc and Dec
Expanding Brackets
(a2 - b2) = (a-b)(a+b)
(a-b)2 = (a-b)(a-b)
Exponentials
Positive Inc: 3 > 2 > 1 > 0.5
Negative Dec: -3 > -2 > -1 > -0.5
Stretch and Compress
y: Vert Scale by a factor of C
x: Hor Scale by a factor of 1/C
X is flipped: If given c=1/3, expand by 3
Trig Transformations
AmpTrigPeriod(t-Phase)+Avg
Period = 2pi/factored out
Amp = Avg - Min
Avg = Max+Min / 2
Notes:
+2piK
Carbon Dating: C(t) = C(0)e^-0.0001209t
Dep(Indi)
Special Triangles
Conversion Charts
1/proportional decrease thing
Semi Log Graphs
Heart Beat / Volume Surface Area
Arc trig
Conversion Chart
Special Triangles
Basic Graphs
Trig Transformations
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Midterm 2 22:44
Average Rate of Change
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Midterm 2 22:44
F(to – Δt) – f(to) / Δt
Functions
1/x2  Looks like 1/x but top quadrants
e-x^2  Bell Curves
t3 – 27 = (t-3)(t2 + 3t + 9)
ee = 0
f’’(x) = 0 Not Necessarily an Inflection Point
Lim  ∞  Divide by Highest Exponent
1/0 = ∞ // 1/∞ = 0
Limit of Sums = Sum of Limits
ax = axlna
Approaches ∞ faster as x approaches ∞
ex > xx > lnx
Approaches 0 faster as x approaches ∞
e-x > x-x > lnx
Larger x values are faster
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