Calculus Volume 1 2. Limits Search for: 2.3 The Limit LawsLearning Objectives Recognize the basic limit laws. Use the limit laws to evaluate the limit of a function. Evaluate the limit of a function by factoring. Use the limit laws to evaluate the limit of a polynomial or rational funct...
4. ∫audu=aulna+C∫audu=aulna+C 5. ∫sinudu=−cosu+C∫sinudu=−cosu+C 6. ∫cosudu=sinu+C∫cosudu=sinu+C 7. ∫sec2udu=tanu+C∫sec2udu=tanu+C 8. ∫csc2udu=−cotu+C∫csc2udu=−cotu+C 9. ∫secutanudu=secu+C∫secutanudu=secu+C 10. ∫cscuc...
Calculus Volume 1 4. Applications of Derivatives Search for: 4.4 The Mean Value TheoremLearning Objectives Explain the meaning of Rolle’s theorem. Describe the significance of the Mean Value Theorem. State three important consequences of the Mean Value Theorem. The Mean Value Theorem is one of...
Calculus Volume 1Table of Contents Preface 1. Functions and Graphs 1 Introduction 1.1 Review of Functions 1.2 Basic Classes of Functions 1.3 Trigonometric Functions 1.4 Inverse Functions 1.5 Exponential and Logarithmic Functions Chapter 1 Review Exercises 2. Limits 2 Introduction 2.1 A...
Calculus Volume 1 3. Derivatives Search for: 3.5 Derivatives of Trigonometric FunctionsLearning Objectives Find the derivatives of the sine and cosine function. Find the derivatives of the standard trigonometric functions. Calculate the higher-order derivatives of the sine and cosine.One...
Calculus Volume 1 3. Derivatives Search for: 3.3 Differentiation RulesLearning Objectives State the constant, constant multiple, and power rules. Apply the sum and difference rules to combine derivatives. Use the product rule for finding the derivative of a product of functions. Use the quotient...
Calculus Volume 1 5. Integration Search for: 5.1 Approximating AreasLearning Objectives Use sigma (summation) notation to calculate sums and powers of integers. Use the sum of rectangular areas to approximate the area under a curve. Use Riemann sums to approximate area. Archimedes was fascinated...
Calculus Volume 1 6. Applications of Integration Search for: 6.5 Physical ApplicationsLearning Objectives Determine the mass of a one-dimensional object from its linear density function. Determine the mass of a two-dimensional circular object from its radial density function. Calculate the work done...
Calculus Volume 1 3. Derivatives Search for: 3.8 Implicit DifferentiationLearning Objectives Find the derivative of a complicated function by using implicit differentiation. Use implicit differentiation to determine the equation of a tangent line. We have already studied how to find equations of tangent...
Calculus Volume 1 6. Applications of Integration Search for: 6.4 Arc Length of a Curve and Surface AreaLearning Objectives Determine the length of a curve, y=f(x),y=f(x), between two points. Determine the length of a curve, x=g(y),x=g(y), between two points. Find th...