MATH 106 - Calculus - Midterm 1
Bu ders hakkında
Calculus dersimize hoş geldiniz. Bu ders alacağınız tüm matematik derslerinin temelini oluşturacak olması sebebiyle oldukça önemli bir yere sahip. Fakat endişe etmenize hiç gerek yok. Bu dersten en yüksek verimi alabilmeniz için paketimizi şu şekilde kurguladık:
- Öncelikle konuları dikkatlice ayırdık ve çok detaylı bir şekilde ve herkes ilk defa öğreniyormuş gibi anlattık,
- Anlattığımız her konunun altına konuyu destekleyici örnekler çözdük ve bunu yaparken hiçbir adımı atlamadan ve yapılan işlemleri silmeden yaptık,
- Çözülen soruları kafanızda daha iyi canlandırabilmeniz için Wolfram Alpha, Desmos, Geogebra gibi uygalamalar ile grafikler çizerek destekledik,
- Çözdüğümüz örnekleri de kolaydan zora doğru sıraladık, bu sayede öğrenme aşamasında eksik bir şey kalmadığına emin olduk,
- Son 15 yılın sınav sorularını derledik ve farklı tarzda olanların tamamını paketimize ekledik,
- MIT gibi oldukça kaliteli sorular üreten üniversitelerin de beğendiğimiz sorularını paketimize dahil ettik,
Ders paketimizi hiçbir şeyi atlamadan adım adım izleyerek bu dersten en yüksek verimi ve sınavlardan en yüksek notları alacağınıza eminiz. Hepinize başarılar dileriz.
Eğitmenler
Fatih Hoca
MATH 106
Herkese merhaba, ben Fatih Hoca. Üniversiteyi birincilikle tamamladıktan sonra 2008-2014 yılları arasında Koç Üniversitesi'nde Yüksek Lisans ve Doktora eğitimleri aldım ve birçok dersin asistanlığını yaptım. 22 senedir binlerce öğrenciye "General Physics I, General Physics II, Finite Mathematics, Calculus, Linear Algebra, Multivariable Calculus, Differentiable Equations" derslerinde yardımcı oldum ve bundan sonra da yanlarında olmaya devam edeceğim.
(4.9)
Önerilen Dersler
Konular
Test Yourself Before You Study
EXAM - Calculus
EXAM - Calculus
Calculus Preliminaries
Functions and Models
The Vertical Line Test
Piecewise Defined Functions
Symmetry
Increasing and Decreasing Functions
Polynomials
Power Functions
Rational Functions
Algebraic Functions
Trigonometric Functions
Transformation of Functions
Example 1
Example 2
Example 3
Combination of Functions
Example 4
Example 5
Exponential Functions
Law of Exponents
The Number "e"
Inverse Functions and Logarithms
How to Find the Inverse of a Function
Logarithmic Functions
Law of Logarithms
Natural Logarithms
Change of Base Formula
Graph and Growth of the Natural Logarithm
Inverse Trigonometric Functions
Limit
Introduction to Limit
One-Sided Limits
A Very Important Theorem
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Formal Definition of Limit
Undefined Values
Example 10
Solving Limits
Properties of Limits
Example 1-6
Solving with Substitution
Example 7
Example 8
Example 9
Solving with Factoring
Example 10
Example 11
Example 12
Example 13
Example 14
Solving with Conjugate Method
Example 15
Example 16
Example 17
Example 18
Example 19
Solving with Substitution
Solving
SQ
Limits of Trigonometric Functions
Very Important Limits
Example 1-2
Example 3-4
Example 5-6
Example 7-8
Squeeze (Sandwich) Theorem
Squeeze (Sandwich) Theorem
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
SSSS
Limits at Infinity - Infinite Limits and Asymptotes
Limits at Infinity and Horizontal Asymptotes
Rules for Horizontal Asymptotes
Example 1 (N<D)
Example 2 (N>D)
Example 3 (N=D)
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Infinite Limits and Vertical Asymptotes
Example 11
Example 12
Example 13
Example 14
Oblique Asymptotes
Example 17
Example 18
Example 15
Example 16
Example 19
Example 20
Continuity
Definition of Continuity
Example 1
Example 3
Example 2
Example 4
Point (Removable) Discontinuities
Does the Limit Exist at a Point Discontinuity?
Example 5
Piecewise Defined Functions
Jump Discontinuities
Does the Limit Exist at a Jump Discontinuity?
Infinite Discontinuities
Does the Limit Exist at an Infinite Discontinuity?
Endpoint Discontinuities
Does the Limit Exist at an Infinite Discontinuity?
Intermediate Value Theorem
Intermediate Value Theorem
Vital Steps for IVT Problems
Example 1
Example 2
Example 3
Another Approach for the Previous Problem
A Very Different Type of IVT Problem
Differentiation
Definition of Derivative
Example 1
Example 2
Example 3
Example 4
Example 5
Proof of the Derivative of Sin(x)
Differentiation Rules
Differentiation Rules
Example 1-6
Product Rule
Product Rule with Three or More Functions
Quotient Rule
Important Derivatives
Derivatives of Exponential Functions
Derviatives of Trigonometric Functions
Derivatives of Inverse Trigonometric Functions
Derivatives of Logarithmic Functions
The Chain Rule
Chain Rule
Chain Rule with Power Rule
Chain Rule with Trigonometric, Logarithmic and Exponential Functions
Chain Rule with Product Rule
Chain Rule with Quotient Rule
Implicit Differentiation
Implicit Differentiation
Example 1
Example 2
Example 3
Example 4
Problem Type Implicit Differentiation Example 5
Problem Type Implicit Differentiation Example 6
Logarithmic Differentiation
Logarithmic Differentation
Example 1-2
Example 3-4
Limit or Derivative ?
Limit or Derivative ?
Example 1
Example 2
Example 3
A Very Hard Example 4
Differentiability
Differentiability
Example 1
Example 2
Example 3
Example 4
Tangent and Normal Lines
Line Equation
Example 1
Tangent Lines
Example 2
Example 3
Example 4
Normal Lines
Example 5
Tangent Lines with Implicit Differentiation
Example 6
Example 7
Example 8
Mean Value Theorem
Mean Value Theorem
Rolle's Theorem
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Indeterminate Forms and L'Hospital's Rule
Indeterminate Forms
Case 1 - Indeterminate Form of 0/0
L'Hospital's Rule
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Case 2 - Indeterminate Form of ∞/∞
Example 7
Example 8
Example 9
Case 3 - Indeterminate Form of 0.∞
Example 10
Example 11
Example 12
Example 13
Case 4 - Indeterminate Form of ∞-∞
Example 14
Example 15
Example 16
Example 17
Case 5 - Indeterminate Form of 0^0
Example 18
Example 19
Example 20
Example 21
Example 22
Case 6 - Indeterminate Form of ∞^0
Example 23
Example 24
Example 25
Example 26
Example 27
Case 7 - Indeterminate Form of 1^∞
Example 28
Example 29
Example 31
Example 30
Example 32
Extreme Values
Absolute Extreme Values
Critical Number
Local Extreme Values
The Closed Interval Theorem
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
What Does f' Say About f ?
The First Derivative Test
Example 7
Example 8
Example 9
Example 10
What Does f'' Say About f ?
The Second Derivative Test
Example 11
Example 12
Example 13
Example 14
Sketching the Graph of a Function
Sketching the Graph of a Function
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Optimization Problems
Steps in Solving Optimization Problems
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Test Yourself Again After You Study
EXAM - Calculus
EXAM - Calculus
Past Midterm I Questions
Example 1 - Limit
Example 2 - Limit
Example 3 - Limit
Example 4 - Limit
Example 5 - Limit
Example 6 - Limit
Example 7 - Limit
Example 8 - Limit
Example 9 - Limit
Example 10 - Limit
Example 11 - Limit
Example 12 - Limit
Example 13 - Limit
Example 14 - Limit
Example 15 - Limit
Example 16 - Limit
Example 17 - Squeeze Theorem
Example 18 - Squeeze Theorem
Example 19 - Squeeze Theorem
Example 20 - Squeeze Theorem
Example 21 - Squeeze Theorem
Example 22 - Asymptotes
Example 23 - Asymptotes
Example 24 - Asymptotes
Example 25 - Asymptotes
Example 26 - Continuity
Example 27 - Continuity
Example 28 - Continuity
Example 29 - Continuity
Example 30 - Intermediate Value Theorem
Example 31 - Intermediate Value Theorem
Example 32 - Intermediate Value Theorem
Example 33 - Intermediate Value Theorem
Example 34 - Intermediate Value Theorem
Example 35 - Intermediate Value Theorem
Example 36 - Definition of Derivative
Example 37 - Definition of Derivative
Example 38 - Definition of Derivative
Example 39 - Implicit Differentiation
Example 40 - Implicit Differentiation
Example 41 - Implicit Differentiation
Example 42 - Implicit Differentiation
Example 43 - Logarithmic Differentiation
Example 44 - Logarithmic Differentiation
Example 45 - Logarithmic Differentiation
Example 46 - Logarithmic Differentiation
Example 47 - Logarithmic Differentiation
Example 48 - Limit or Derivative?
Example 49 - Limit or Derivative?
Example 50 - Limit or Derivative?
Example 51 - Differentiability
Example 52 - Differentiability
Example 53 - Differentiability
Example 54 - Differentiability
Example 55 - Line Equation
Example 56 - Line Equation
Example 57 - Line Equation
Example 58 - Line Equation
Example 59 - Line Equation
Example 60 - Line Equation
Example 61 - Line Equation
Exam Questions from Other Universities
Example 1 - Limit
Example 2 - Limit
Example 3 - Limit
Example 4 - Limit
Example 5 - Limit
Example 6 - Limit
Example 7 - Limit
Example 8 - Limit
Example 9 - Squeeze Theorem
Example 10 - Squeeze Theorem
Example 11 - Asymptotes
Example 12 - Continuity
Example 13 - Continuity
Example 14 - Intermediate Value Theorem
Example 15 - Definition of Derivative
Example 16 - Implicit Differentiation
Example 17 - Implicit Differentiation
Example 18 - Logarithmic Differentiation
Example 19 - Logarithmic Differentiation
Example 20 - Limit or Derivative?
Example 7 - Differentiability
Example 22 - Differentiability
Example 23 - Line Equation
Example 24 - Line Equation
Challenging Questions
Example 1 - Limit
Example 2 - Limit
Example 3 - Squeeze Theorem
Example 4 - Asymptotes
Example 5 - Continuity
Example 6 - Intermediate Value Theorem
Example 7 - Definition of Derivative
Example 8 - Definition of Derivative
Example 9 - Implicit Differentiation
Example 10 - Logarithmic Differentiation
Example 11 - Limit or Derivative?
Example 12 - Differentiability
Example 13 - Line Equation
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Konular
Test Yourself Before You Study
EXAM - Calculus
EXAM - Calculus
Calculus Preliminaries
Functions and Models
The Vertical Line Test
Piecewise Defined Functions
Symmetry
Increasing and Decreasing Functions
Polynomials
Power Functions
Rational Functions
Algebraic Functions
Trigonometric Functions
Transformation of Functions
Example 1
Example 2
Example 3
Combination of Functions
Example 4
Example 5
Exponential Functions
Law of Exponents
The Number "e"
Inverse Functions and Logarithms
How to Find the Inverse of a Function
Logarithmic Functions
Law of Logarithms
Natural Logarithms
Change of Base Formula
Graph and Growth of the Natural Logarithm
Inverse Trigonometric Functions
Limit
Introduction to Limit
One-Sided Limits
A Very Important Theorem
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Formal Definition of Limit
Undefined Values
Example 10
Solving Limits
Properties of Limits
Example 1-6
Solving with Substitution
Example 7
Example 8
Example 9
Solving with Factoring
Example 10
Example 11
Example 12
Example 13
Example 14
Solving with Conjugate Method
Example 15
Example 16
Example 17
Example 18
Example 19
Solving with Substitution
Solving
SQ
Limits of Trigonometric Functions
Very Important Limits
Example 1-2
Example 3-4
Example 5-6
Example 7-8
Squeeze (Sandwich) Theorem
Squeeze (Sandwich) Theorem
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
SSSS
Limits at Infinity - Infinite Limits and Asymptotes
Limits at Infinity and Horizontal Asymptotes
Rules for Horizontal Asymptotes
Example 1 (N<D)
Example 2 (N>D)
Example 3 (N=D)
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Infinite Limits and Vertical Asymptotes
Example 11
Example 12
Example 13
Example 14
Oblique Asymptotes
Example 17
Example 18
Example 15
Example 16
Example 19
Example 20
Continuity
Definition of Continuity
Example 1
Example 3
Example 2
Example 4
Point (Removable) Discontinuities
Does the Limit Exist at a Point Discontinuity?
Example 5
Piecewise Defined Functions
Jump Discontinuities
Does the Limit Exist at a Jump Discontinuity?
Infinite Discontinuities
Does the Limit Exist at an Infinite Discontinuity?
Endpoint Discontinuities
Does the Limit Exist at an Infinite Discontinuity?
Intermediate Value Theorem
Intermediate Value Theorem
Vital Steps for IVT Problems
Example 1
Example 2
Example 3
Another Approach for the Previous Problem
A Very Different Type of IVT Problem
Differentiation
Definition of Derivative
Example 1
Example 2
Example 3
Example 4
Example 5
Proof of the Derivative of Sin(x)
Differentiation Rules
Differentiation Rules
Example 1-6
Product Rule
Product Rule with Three or More Functions
Quotient Rule
Important Derivatives
Derivatives of Exponential Functions
Derviatives of Trigonometric Functions
Derivatives of Inverse Trigonometric Functions
Derivatives of Logarithmic Functions
The Chain Rule
Chain Rule
Chain Rule with Power Rule
Chain Rule with Trigonometric, Logarithmic and Exponential Functions
Chain Rule with Product Rule
Chain Rule with Quotient Rule
Implicit Differentiation
Implicit Differentiation
Example 1
Example 2
Example 3
Example 4
Problem Type Implicit Differentiation Example 5
Problem Type Implicit Differentiation Example 6
Logarithmic Differentiation
Logarithmic Differentation
Example 1-2
Example 3-4
Limit or Derivative ?
Limit or Derivative ?
Example 1
Example 2
Example 3
A Very Hard Example 4
Differentiability
Differentiability
Example 1
Example 2
Example 3
Example 4
Tangent and Normal Lines
Line Equation
Example 1
Tangent Lines
Example 2
Example 3
Example 4
Normal Lines
Example 5
Tangent Lines with Implicit Differentiation
Example 6
Example 7
Example 8
Mean Value Theorem
Mean Value Theorem
Rolle's Theorem
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Indeterminate Forms and L'Hospital's Rule
Indeterminate Forms
Case 1 - Indeterminate Form of 0/0
L'Hospital's Rule
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Case 2 - Indeterminate Form of ∞/∞
Example 7
Example 8
Example 9
Case 3 - Indeterminate Form of 0.∞
Example 10
Example 11
Example 12
Example 13
Case 4 - Indeterminate Form of ∞-∞
Example 14
Example 15
Example 16
Example 17
Case 5 - Indeterminate Form of 0^0
Example 18
Example 19
Example 20
Example 21
Example 22
Case 6 - Indeterminate Form of ∞^0
Example 23
Example 24
Example 25
Example 26
Example 27
Case 7 - Indeterminate Form of 1^∞
Example 28
Example 29
Example 31
Example 30
Example 32
Extreme Values
Absolute Extreme Values
Critical Number
Local Extreme Values
The Closed Interval Theorem
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
What Does f' Say About f ?
The First Derivative Test
Example 7
Example 8
Example 9
Example 10
What Does f'' Say About f ?
The Second Derivative Test
Example 11
Example 12
Example 13
Example 14
Sketching the Graph of a Function
Sketching the Graph of a Function
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Optimization Problems
Steps in Solving Optimization Problems
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Test Yourself Again After You Study
EXAM - Calculus
EXAM - Calculus
Past Midterm I Questions
Example 1 - Limit
Example 2 - Limit
Example 3 - Limit
Example 4 - Limit
Example 5 - Limit
Example 6 - Limit
Example 7 - Limit
Example 8 - Limit
Example 9 - Limit
Example 10 - Limit
Example 11 - Limit
Example 12 - Limit
Example 13 - Limit
Example 14 - Limit
Example 15 - Limit
Example 16 - Limit
Example 17 - Squeeze Theorem
Example 18 - Squeeze Theorem
Example 19 - Squeeze Theorem
Example 20 - Squeeze Theorem
Example 21 - Squeeze Theorem
Example 22 - Asymptotes
Example 23 - Asymptotes
Example 24 - Asymptotes
Example 25 - Asymptotes
Example 26 - Continuity
Example 27 - Continuity
Example 28 - Continuity
Example 29 - Continuity
Example 30 - Intermediate Value Theorem
Example 31 - Intermediate Value Theorem
Example 32 - Intermediate Value Theorem
Example 33 - Intermediate Value Theorem
Example 34 - Intermediate Value Theorem
Example 35 - Intermediate Value Theorem
Example 36 - Definition of Derivative
Example 37 - Definition of Derivative
Example 38 - Definition of Derivative
Example 39 - Implicit Differentiation
Example 40 - Implicit Differentiation
Example 41 - Implicit Differentiation
Example 42 - Implicit Differentiation
Example 43 - Logarithmic Differentiation
Example 44 - Logarithmic Differentiation
Example 45 - Logarithmic Differentiation
Example 46 - Logarithmic Differentiation
Example 47 - Logarithmic Differentiation
Example 48 - Limit or Derivative?
Example 49 - Limit or Derivative?
Example 50 - Limit or Derivative?
Example 51 - Differentiability
Example 52 - Differentiability
Example 53 - Differentiability
Example 54 - Differentiability
Example 55 - Line Equation
Example 56 - Line Equation
Example 57 - Line Equation
Example 58 - Line Equation
Example 59 - Line Equation
Example 60 - Line Equation
Example 61 - Line Equation
Exam Questions from Other Universities
Example 1 - Limit
Example 2 - Limit
Example 3 - Limit
Example 4 - Limit
Example 5 - Limit
Example 6 - Limit
Example 7 - Limit
Example 8 - Limit
Example 9 - Squeeze Theorem
Example 10 - Squeeze Theorem
Example 11 - Asymptotes
Example 12 - Continuity
Example 13 - Continuity
Example 14 - Intermediate Value Theorem
Example 15 - Definition of Derivative
Example 16 - Implicit Differentiation
Example 17 - Implicit Differentiation
Example 18 - Logarithmic Differentiation
Example 19 - Logarithmic Differentiation
Example 20 - Limit or Derivative?
Example 7 - Differentiability
Example 22 - Differentiability
Example 23 - Line Equation
Example 24 - Line Equation
Challenging Questions
Example 1 - Limit
Example 2 - Limit
Example 3 - Squeeze Theorem
Example 4 - Asymptotes
Example 5 - Continuity
Example 6 - Intermediate Value Theorem
Example 7 - Definition of Derivative
Example 8 - Definition of Derivative
Example 9 - Implicit Differentiation
Example 10 - Logarithmic Differentiation
Example 11 - Limit or Derivative?
Example 12 - Differentiability
Example 13 - Line Equation
