Calculus 1 review

Comprehensive Calculus Notes & Exam Review Guide (20 Pages) These handwritten calculus notes are a complete, detailed, and carefully organized study resource covering the core concepts of introductory university-level calculus. Designed for students taking Calculus I or preparing for midterms/finals, the notes combine lecture explanations, formulas, worked examples, review guides, problem-solving methods, and visual diagrams all in one place. The document spans multiple major calculus topics and presents them in a clear, student-friendly format that makes difficult concepts easier to understand and review quickly before exams, quizzes, homework assignments, or placement tests. What’s Included: • Functions and Graphs Function notation and evaluation Piecewise functions Even and odd functions Polynomial, rational, logarithmic, and root functions Domains and ranges Transformations and graph behavior Composition of functions Important parent graphs and asymptotes • Limits and Continuity Limit laws and substitution methods Infinite limits and limits at infinity One-sided limits Squeeze theorem Intermediate Value Theorem Continuity and discontinuities Vertical and horizontal asymptotes Evaluating complex limits step-by-step • Derivatives and Differentiation Definition of the derivative Difference quotient Tangent lines and instantaneous rate of change Product rule Quotient rule Chain rule Implicit differentiation Higher-order derivatives Related rates and applications Linear approximations and differentials • Exponential, Logarithmic, and Inverse Functions Properties of logarithms Derivatives of logs and exponentials Inverse functions and inverse trig functions Logarithmic differentiation Restricting domains for inverses Change of base formula • Applications of Derivatives Optimization problems Critical points Mean Value Theorem Rolle’s Theorem Increasing/decreasing intervals Concavity and inflection points First and second derivative tests Curve sketching techniques Global vs local extrema • Integrals and Antiderivatives Antiderivative rules and formulas Definite and indefinite integrals Riemann sums Sigma notation Fundamental Theorem of Calculus Net change theorem Area under curves Average value of a function Velocity, displacement, and distance applications These notes are not just copied formulas — they contain explanations, reasoning, shortcuts, reminders, annotations, visual sketches, highlighted exam tips, and worked examples that reflect actual classroom learning and problem-solving strategies. They are especially useful for students who struggle with textbook explanations and want material written in a more intuitive and understandable way. The layout makes them ideal for: Exam review Homework help Learning difficult topics quickly Creating study guides or flashcards Supplementing lecture material Self-studying calculus