# Textbook Notes for MATH 2A at University of California - Irvine (UC-IRVINE)

## Premium Notes

UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 31: 44080-Math 2A Lecture 31 Notes-Antiderivatives

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture Notes - Lecture 30: Cist, Hedeby Stones, Avea

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 29: 44080-Math 2A Lecture 29-L' Hopitals Rule

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture Notes - Lecture 28: Minimax

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 27: 44080-Math 2A Lecture 27-Mean Value Theorem & Increasing and Decreasing Test

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 26: 44080-Math 2A Lecture 26 Notes-Rolle's Theorum

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture Notes - Lecture 24: Minimax, Mox Fuel

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture Notes - Lecture 23: Maxima And Minima, Minimax

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 22: 44080-Math 2A Lecture 22 Notes-Linear Approximation and Differentials

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 19: 44080-Math 2A Lecture 19 Notes-Related Rates

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 18: 44080-Math 2A Lecture 18 Notes-Exponential Growth and Decay

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 4: 44080-Math 2A Lecture 4 Notes-Limits and Infinite Limits

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 3: 44080-Math 2A Lecture 3 Notes-Limits and Derivatives

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 1: 44080-Math 2A Lecture 1 Notes-Functions and Models

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Study Guide - Fall 2018, Comprehensive Midterm Notes -

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 17: 44080-Math 2A Lecture 17 Notes-Derivatives of Logarithmic Functions

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 15: 44080-Math 2A Lecture 15 Notes-Graphing Derivative Functions

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 12: 44080-Math 2A Lecture 12 Notes-Derivatives of a Function

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 9: 44080-Math 2A Lecture 9 Notes-Rate of Change

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 14: 44080-Math 2A Lecture 14 Notes-Derivatives

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture Notes - Lecture 16: Implicit Function

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 10: 44080-Math 2A Lecture 10 Notes-Derivatives as a Function

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 5: 44080-Math 2A Lecture 5 Notes-Limits

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 8: 44080-Math 2A Lecture 8 Notes-Limits at Infinity

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 7: 44080-Math 2A Lecture 7 Notes-Continuity

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 13: 44080-Math 2A Lecture 13 Notes-Formulas for Derivatives

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 6: 44080-Math 2A Lecture 6 Notes-Continuity

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UC-IRVINEMATH 2AJESSIE, D.Fall

## MATH 2A Lecture 2: 44080 - Lecture 2 - Inverse and Logarithmic Function

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UC-IRVINEMATH 2AAghavni SimonyanWinter

## MATH 2A Lecture 29: Optimization Problems cont. + AntiDerivatives

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UC-IRVINEMATH 2AAghavni SimonyanWinter

## MATH 2A Lecture 28: Summary of Curve Sketching cont. + Optimization Problems

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UC-IRVINEMATH 2AAghavni SimonyanWinter

## MATH 2A Lecture 27: Summary of Curve Sketching

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UC-IRVINEMATH 2AAghavni SimonyanWinter

## MATH 2A Lecture 26: Intermediate Forms and L'Hospital Rule

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UC-IRVINEMATH 2AAghavni SimonyanWinter

## MATH 2A Lecture 25: How Derivatives Affect Shape of Graph

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UC-IRVINEMATH 2AAghavni SimonyanWinter

## MATH 2A Lecture 24: The Mean Value Theorem

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UC-IRVINEMATH 2AAghavni SimonyanWinter

## MATH 2A Lecture 23: Minimum and Maximum Values

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UC-IRVINEMATH 2AAghavni SimonyanWinter

## MATH 2A Lecture 20: Newton's Law of Cooling

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UC-IRVINEMATH 2AAghavni SimonyanWinter

## MATH 2A Lecture 18: Exponential Growth and Decay

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UC-IRVINEMATH 2AAghavni SimonyanWinter

## MATH 2A Lecture 17: Derivative of Logarithmic Functions

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UC-IRVINEMATH 2AAghavni SimonyanWinter

## MATH 2A Lecture 16: 3.5 Implicit DIfferentiation

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UC-IRVINEMATH 2AAghavni SimonyanWinter

## MATH 2A Lecture 15: The Chain Rule

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UC-IRVINEMATH 2AAghavni SimonyanWinter

## MATH 2A Lecture 14: Derivatives of Trigonometric Functions

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UC-IRVINEMATH 2AAghavni SimonyanWinter

## MATH 2A Lecture 13: 3.1 Derivatives of Polynomials and Exponential Functions

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 31: Math 2A Lecture 31: Final Review

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 30: Math 2A Lecture 30: Antiderivatives ctn & Final Review

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 29: Math 2A Lecture 29: Optimization & Antiderivatives

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 28: Math 2A Lecture 28

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 27: Math 2A Lecture 27: L'Hopital's Rule

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture Notes - Lecture 26: Maxima And Minima, Minimax, Inflection

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Math 2a lecture 26: first and second derivative test. : find the local maximum values of g(x) at x + 2 sinx, from 0 x 2. 4/3 g"(x) changes from positiv
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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 24: Math 2A Lecture 24

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 23: Math 2A Lecture 23

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 22: Math 2A Lecture 22

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 19: Math 2A Lecture 19: Related Rates and Linear Approximations

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 18: Math 2A Lecture 18: Exponential Growth and Decay

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 17: Math 2A Lecture 17

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Study Guide - Fall 2018, Comprehensive Midterm Notes - Graph Of A Function, Integer, Transcendentals

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A is called the base and a > 0. A n = a * a * a. Rules of exponents: a x+y = a x * a y : adding exponents is the same as multiplying the exponential fu
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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture Notes - Lecture 16: Implicit Function

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 15: Math 2A Lecture 15: Implicit Differentiation

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 14: Math 2A Lecture 14: Chain Rule

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 13: Math 2A Lecture 13: More Derivatives and Derivatives of Trig Functions

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture Notes - Lecture 12: Tangent, Differentiable Function, Power Rule

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture Notes - Lecture 10: Intermediate Value Theorem

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: if f(x) lim h 0 f(x+h) f(x) h h(2+(x+h)(2+x) = (3)/((2+x) 2 ) exists, we say that f is differentiable at x=a. : find f (x) where f(x) = (((1 (x+h))/(
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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture Notes - Lecture 8: Squeeze Theorem

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture Notes - Lecture 9: Tangent, Hyperbola

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 8: Math 2A Lecture 8: Limits at Infinity & Horizontal Asymptotes

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 1: MATH 2A - Lecture 1 - Four ways to represent a function

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Math 2a - lecture 1 - four ways to represent a function. A function f is a rule that assigns to each element x in a set d, exactly one. For each x ther
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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture Notes - Lecture 5: Logarithm, Inverse Function, Farad

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture Notes - Lecture 2: Algebraic Function, Cube Root, Logarithm

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Math 2a - lecture 2 - mathematical models and different types of functions. A mathematical model is a mathematical description (often by means of funct
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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 4: MATH 2A - Lecture 4 - Exponential Functions

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Math 2a - lecture 4 - exponential functions. We previously defined a function in the form of variable). Do not confuse exponential functions with power
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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture Notes - Lecture 6: Tangent

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Math 2a - lecture 6 - tangent line problem & velocity problem. Suppose that we have a curve like y=x and we want to know the slope of the tangent line
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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture Notes - Lecture 3: Function Composition, Farad

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Math 2a - lecture 3 - new functions from old functions. By applying certain transformations to the graph of a given function, we can obtain the graph o
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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture Notes - Lecture 7: Intermediate Value Theorem

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F is not continuous at x = 3. Where are the following functions discontinuous? a) b) f(x)= (x^2 -x -2) / (x-2) x=2 f(x) = 1/x^2 if x 0 x = 0. Therefore
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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture Notes - Lecture 6: Power Law

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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture Notes - Lecture 5: Asymptote

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The limit of f(x) as x approaches a is l. Y = 2x graph: https://people. richland. edu/james/lecture/m116/logs/2x. gif y=log 2 x graph: https://upload.
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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 4: Math 2A Lecture 4 and Discussion Notes- Functions ctn.

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UC-IRVINEMATH 2AShuhao CaoFall

## MATH 2A Lecture Notes - Lecture 3: Logarithm, Inverse Function

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Week 1 lecture 3 functions (cont. ) and compound interest. Imagine this scenario: 100% annual interest rate, what the bank pays you annually, there is
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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture Notes - Lecture 3: Inverse Function, Trigonometric Functions

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Types of functions: there are five basic types of functions, trigonometric functions (sinx, cosx, etc. , polynomial functions ( x 2 + x + 3, etc. , exp
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UC-IRVINEMATH 2ALiu, WFall

## MATH 2A Lecture 2: MATH2A Lecture 2- Exponential Functions and Inverse Functions

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A is called the base and a > 0. A n = a * a * a. Rules of exponents: a x+y = a x * a y : adding exponents is the same as multiplying the exponential fu
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UC-IRVINEMATH 2AShuhao CaoFall

## MATH 2A Lecture 2: Math 2A (44095) - Lecture 2 - Functions(cont.)

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UC-IRVINEMATH 2AShuhao CaoFall

## MATH 2A Lecture Notes - Lecture 1: Set Notation, Piecewise

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[-3, 5] = this states that x is a value from -3 to 5 including 3 and 5; (cid:885)(cid:3409) (cid:1876)(cid:3409)(cid:887: means that (cid:885)<(cid:187
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UC-IRVINEMATH 2AKenn HuberFall

## Math 2A Chapter 4.4: L'Hopital's Rule

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UC-IRVINEMATH 2AGerman A Enciso RuizFall

## MATH 2A Chapter 2.1-2.2: Lecture 5

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UC-IRVINEMATH 2AKenn HuberSummer

## MATH 2A Chapter 1.5-1.6: 1.5 - 1.6

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UC-IRVINEMATH 2AGerman A Enciso RuizFall

## MATH 2A Chapter 3.3-3.4: Lecture 13, 14

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UC-IRVINEMATH 2AGerman A Enciso RuizFall

## MATH 2A Chapter 2.3-2.6: Lecture 6-8

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UC-IRVINEMATH 2AGerman A Enciso RuizFall

## MATH 2A Chapter 1.5: Lecture 4

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UC-IRVINEMATH 2AKenn HuberFall

## Math 2A Chapter 4.1: Extrema

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UC-IRVINEMATH 2AKenn HuberFall

## MATH 2A Chapter Notes - Chapter 4.2: Georgia State Route 2

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UC-IRVINEMATH 2AKenn HuberFall

## Math 2A Chapter 1.3: New functions (from odd functions)

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UC-IRVINEMATH 2ACatherine FamigliettiFall

## MATH 2A Chapter 3.1: Section 3.1

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UC-IRVINEMATH 2ACatherine FamigliettiFall

## MATH 2A Chapter 2.8: Section 2.8

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UC-IRVINEMATH 2AYuki TakahashiFall

## Math 2A Chapter 2: Math 2A Calculus 2.5

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