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

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12 Aug 2016

School

Department

Course

Professor

Midterm 1 22:44

Intervals of Inc and Dec

Read from Left to Right

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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