MATH 151 • Tüm Sınavlar • Calculus I
Atılım Üniversitesi MATH 151 (Calculus I) Midterm I sınavına hazırlık paketi.
İşlenen konular: Functions (Domain-Composite-Inverse), Graph of Functions (Shifting & Scaling), Limits of Functions, The Squeeze (Sandwich) Theorem, Limits at Infinity and Infinite Limits, Asymptotes, Limits of Trigonometric Functions, Continuity and Discontinuity, Intermediate Value Theorem, The Limit Definition of Derivatives, Differentiability, Differentiation Rules (Product, Quotient, Exponential), Higher Order Differentiation, Derivative of Trigonometric Functions, The Chain Rule, Tangent Line Equations, Implicit Differentiation, The Mean Value Theorem.
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Eğitmenler
Dorukhan Özcan
Co-Founder & CEO
Unicourse şirketinin kurucu ortağıyım. 2016 senesinde Galatasaray Lisesinden mezun oldum. Geçtiğimiz dört sene içerisinde 2000 saatten fazla ders anlattım. Anlattığım dersler sırasıyla; Calculus, Çok değişkenli Calculus, Lineer Cebir, Differansiyel Denklemler, Uygulamalı İstatistik ve Stokastik Modelleme dersleridir. Doping Hafıza şirketinde 2017 - 2022 seneleri arasında CEO danışmanlığı yaptım. Koç Üniversitesi Endüstri Mühendisliği ve Ekonomi çift anadal programını tam burslu olarak, 3.96/4.00 not ortalamasıyla bitirdim. Kadıköy Modalıyım.
Tolga Temiz
Eğitmen
2016 senesinde başladığım Koç Üniversitesi Matematik bölümünden 2020 senesinde fakülte üçüncüsü olarak mezun oldum. Lisans ve yüksek lisans eğitimlerim boyunca çeşitli derslerde asistanlık yaptım. 2021'de Koç Üniversitesi'nde Matematik yüksek lisansına başladım ve 2023 yılında mezun oldum. Şimdi Michigan State Üniversitesi'nde doktora yapıyorum. Topoloji alanıyla ilgilenmekteyim.
Kerem Başol
Eğitmen
2019 senesinde Koç Üniversitesi Matematik bölümüne başladım. Geçtiğimiz senelerde Calculus ve Linear Algebra derslerinde Tutor ve Teaching Assistant pozisyonlarında görev aldım. Halen Koç Üniversitesi Matematik ve Bilgisayar Mühendisliği çift anadal programını 4.00/4.00 ortalamayla fakülte birincisi olarak sürdürüyorum. Trigonometrik fonksiyonların elips üzerinde nasıl tanımlanabileceğini merak etmemle başlayan Matematik tutkumu aktarmak için Unicourse Matematik Zümresine katıldım.
Konular
Functions (Domain-Composite-Inverse)
7 konu anlatımı
Domain of Functions
Domain of Exponential & Logarithms
Even and Odd Functions
The Vertical & Horizontal Line Tests
Composite Functions
Inverse of Functions
Inverse of Exponential & Logarithms
Graph of Functions (Shifting & Scaling)
6 konu anlatımı · 9 soru
Graph of Functions (Shifting & Scaling)
Graph of Functions I
Graph of Functions II
Graph of Functions III
Graph of Exponential Functions
Graph of Logarithmic Functions
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Limits of Functions
3 konu anlatımı · 10 soru
Limits of Functions
Limits with Absolute Value
Limits Rules
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The Squeeze (Sandwich) Theorem
1 konu anlatımı · 5 soru
The Squeeze (Sandwich) Theorem
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Limits at Infinity and Infinite Limits
4 konu anlatımı · 8 soru
Limits at Infinity I
Limits at Infinity II
Limits at Infinity III
Infinite Limits
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Asymptotes
2 konu anlatımı · 4 soru
Vertical and Horizontal Asymptotes
Oblique Asymptotes
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Limits of Trigonometric Functions
3 konu anlatımı · 6 soru
Limit of Trigonometric Functions I
Limit of Trigonometric Functions II
Limit of Trigonometric Functions III
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Continuity and Discontinuity
2 konu anlatımı · 10 soru
Continuity
Discontinuity and Continuous Extension
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Intermediate Value Theorem
2 konu anlatımı · 6 soru
Intermediate Value Theorem I
Intermediate Value Theorem II
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The Limit Definition of Derivatives
4 konu anlatımı · 8 soru
Rate of Change: Derivative at a Point
Derivative as a Function I
Derivative as a Function II
"Hidden" Derivative
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Differentiability
2 konu anlatımı · 9 soru
Differentiability (with Limit Definition)
Differentiability (without using Limit Definition)
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Differentiation Rules (Product, Quotient, Exponential)
4 konu anlatımı · 12 soru
Power Rule
Derivatives of Exponentials
Product Rule
Quotient Rule
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Higher Order Differentiation
1 konu anlatımı · 3 soru
Higher Order Derivative
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Derivative of Trigonometric Functions
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Derivatives of Trigonometric Functions
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The Chain Rule
2 konu anlatımı · 15 soru
Chain Rule I
Chain Rule II
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Tangent Line Equations
4 konu anlatımı · 13 soru
Equation of a Tangent Line I
Equation of a Tangent Line II
Horizontal and Vertical Tangent
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Challenging: Tangent Line Passes through a Point
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Implicit Differentiation
3 konu anlatımı · 9 soru
Implicit Differentiation I
Implicit Differentiation II
Tangent Lines & Implicit Functions
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The Mean Value Theorem
4 konu anlatımı · 11 soru
Mean Value Theorem I
Mean Value Theorem II
Mean Value Theorem III
Mean Value Theorem IV
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Increasing, Decreasing Functions and Derivative of Inverse Function
2 konu anlatımı · 4 soru
Increasing and Decreasing Functions
Derivative of Inverse
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Past Exam Problems (Konu Sırasıyla)
21 soru
Fall 2024 Exam: Limit without L'Hopital's Rule
Spring 2022 Exam: Limit without L'Hopital's Rule
Fall 2024 Exam: Limit with Absolute Value
Fall 2024 Exam: Limit of Trigonometric Functions
Spring 2022 Exam: Limits of Trigonometric Functions
Spring 2022 Exam: Infinite Limits
Fall 2024 Exam: Limit at Infinity
Spring 2022 Exam: Limit at Infinity
Fall 2024 Exam: Intermediate Value Theorem
Fall 2024 Exam: Continuity and Differentiability
Spring 2022 Exam: Continuity and Differentiability
Fall 2024 Exam: Derivative of Inverse Function
Fall 2024 Exam: Higher Order Differentiation
Fall 2024 Exam: The Chain Rule
Spring 2022 Exam: The Chain Rule
Fall 2024 Exam: Equation of a Tangent Line
Fall 2024 Exam: Implicit Differentiation
Spring 2022 Exam: Tangent Line and Implicit Differentiation
Fall 2024 Exam: Mean Value Theorem
Spring 2022 Exam: Mean Value Theorem
Spring 2022 Exam: Logarithmic Differentiation
Derivative of Inverse Function
1 konu anlatımı · 5 soru
Derivative of Inverse
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Derivative of Inverse Trigonometric Functions
2 konu anlatımı · 10 soru
Inverse Trigonometric Functions
Derivatives of Inverse Trigonometric Functions
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Implicit & Inverse Trigonometric Functions I
Implicit & Inverse Trigonometric Functions II
Implicit & Inverse Trigonometric Functions III
Derivative of Exponentials and Logarithms
1 konu anlatımı · 6 soru
Derivatives of Exponential & Logarithmic Functions
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Logarithmic Differentiation
2 konu anlatımı · 7 soru
Logarithmic Differentiation I
Logarithmic Differentiation II
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Linear Approximation (Linearization)
1 konu anlatımı · 5 soru
Linear Approximation
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Related Rates
2 konu anlatımı · 3 soru
Related Rates I
Related Rates II
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Extreme Values and Critical Points
1 konu anlatımı · 5 soru
Critical Points, Absolute Maximum & Minimum
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Concavity and Inflections
2 konu anlatımı · 7 soru
First Derivative Test & Extremum Values
Second Derivative & Concavity
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Curve Sketching
3 konu anlatımı · 3 soru
Curve Sketching I
Curve Sketching II
Curve Sketching III
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Optimization (Extreme Value) Problems
4 konu anlatımı · 13 soru
Optimization Problems I
Optimization Problems II
Optimization Problems III
Optimization Problems IV
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Challenging Problem
Indeterminate Forms (L'Hopital's Rule)
7 konu anlatımı
Indeterminate Form 1 (0/0)
Indeterminate Form 2 (∞/∞)
Indeterminate Form 3 (0 x ∞)
Indeterminate Form 4 (∞ - ∞)
Indeterminate Form 5 (0^0)
Indeterminate Form 6 (∞^0)
Indeterminate Form 7 (1 ^ ∞)
Antiderivative & Integration Rules
5 konu anlatımı
Integration Rules I
Integration Rules II
Integral of Trigonometric Functions I
Integral of Trigonometric Functions II
Integral of Exponential Functions
Integration with Substitution
7 konu anlatımı · 9 soru
Integration with Substitution
Substitution with Logarithms & Exponentials I
Substitution with Logarithms & Exponentials II
Substitution with Trigonometric Functions 1
Substitution with Trigonometric Functions 2
Substitution with Trigonometric Functions 3
Substitution with Trigonometric Functions 4
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Integration by Parts
6 konu anlatımı · 8 soru
Integration by Part I
Integration by Part II
Integration by Part III
Integration by Part IV
Integration By Part V
Faster Method for Integration by Part
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Integrals of Rational Functions
2 konu anlatımı · 3 soru
Partial Fractions I
Partial Fractions II
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Spring 2024 Exam
7 soru
Indeterminate Forms
Indeterminate Forms
Extreme Values
Related Rates
Basic Integration
Integration by Substitution
Integration by Substitution
(NEW) Fall 2024 Exam
11 soru
Limits of Functions
Limits of Functions
Limits of Functions
Limits of Functions
Indefinite Integrals
Indefinite Integrals
Indefinite Integrals
Indefinite Integrals
Optimization Problem
Related Rates
Sketching Graph
General Exam Review
20 soru
Extreme Values
Curve Sketching
Absolute Maximum and Minimum
Absolute Maximum and Minimum
Linear Approximation
Linear Approximation
Linear Approximation
Spring 2025 Exam: Optimization Problems
Fall 2024 Exam: Optimization Problems
Integration Rules (By Part, Fractions, Substitution)
Integration Rules (By Part, Fractions, Substitution)
Partial Fractions
Partial Fractions
Partial Fractions
Integration by Part
Integration by Part
Integration by Part
Integration by Part
Integration by Part
Integration by Part
Properties of Integration
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Properties of Integration
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Integrals of Rational Functions
2 konu anlatımı · 5 soru
Partial Fractions I
Partial Fractions II
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Inverse Trigonometric Substitution
2 konu anlatımı · 3 soru
Inverse Trigonometric Substitution I
Inverse Trigonometric Substitution II
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Fundamental Theorem of Calculus
3 konu anlatımı · 9 soru
Fundamental Theorem of Calculus I
Fundamental Theorem of Calculus II
FTC and L'Hospital's Rule
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Area between Curves
5 konu anlatımı · 7 soru
Area and Integral
Area between Curves I
Area between Curves II
Area between Curves III
Area between Curves IV
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Improper Integrals
5 konu anlatımı · 8 soru
Intuition of Improper Integrals
Convergence of Improper Integrals
P test for Improper Integrals
Direct Comparison Test 1
Direct Comparison Test 2
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Volume by Integration
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Solids of Revolution-1
Solid of Revolution 2
Solid of Revolution 3
Solid of Revolution 4
Solid of Revolution 5
Arc Length Calculation
1 konu anlatımı · 2 soru
Arc Length Calculation
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Fall 2024 Exam
6 soru
Linearization
Indeterminate Forms (L'Hopital's Rule)
Integration Techniques
Area Between Curves
Volume of Solide of Revolution
Arc length
Spring 2024 Exam
8 soru
Derivative of Trigonometric Functions
Logarithmic Differentiation
Fundamental Theorem of Calculus
Asymptotes
Extremum Value Problem
Integration by Parts
Integration by Substitution
Improper Integral
(NEW) Sınav Provası: Spring 2025 Exam Problems
10 soru
Indeterminate Forms (L'Hopital's Rule)
Limits of Functions
Indeterminate Forms (L'Hopital's Rule)
FTC and Indeterminate Forms
Integrals of Rational Functions
Integration by Parts
Integration by Substitution
Curve Sketching
Extremum Value Problem
Linear Approximation
(NEW) General Exam Review
39 soru
Integration by Substitution
Integration by Substitution
Integration Rules (By Part, Fractions, Substitution)
Integration Rules (By Part, Fractions, Substitution)
Integration by Part
Integration by Part
Integration by Part
Integration by Part
Partial Fractions
Partial Fractions
Partial Fractions
Partial Fractions
Partial Fractions & Substitution
Partial Fractions & Integration by Part
Inverse Trigonometric Substitution
Inverse Trigonometric Substitution & Improper
Inverse Trigonometric Substitution
Inverse Trigonometric Substitution
Improper Integral
Improper Integrals
Improper Integrals
Improper Integral
Improper Integral
Improper Integrals
FTC and L'Hopital's Rule
FTC and L'Hopital's Rule
FTC and Tangent Line
Area between Curves
Area between Curves
Area between Curves
Area between Curves
Area between Curves
Area between Curves
Area between Curves
Integrals (using areas of known functions)
Volume by Integration
Volume by Integration
Volume by Integration
Volume by Integration