51社区

Sections and Exercises refer to the textbook for the course.

Section 2.1 Introduction to Limits

• H01: Skills Warmup: Factoring (1,3,5)
• H02: Given graph of f, find limit (15,16,21,23)
• H03: Given specified limit behavior, sketch graph of f. (47,49)
• H04: Using Theorem 2 Limit Properties to find Limits (33,35,37,41)
• H05: Limits of Rational Functions (59,61,63,73,75)
• H06: Limits of Piecewise-Defined Functions (53,57,91)
• H07: Limits of Difference Quotients (81,83)
• H08: Conceptual Questions (67,68,69,70,71,72)

Section 2.2 Infinite Limits and Limits at Infinity

• H09: Skills Warmup: Line Equations (3,4)
• H10: Given graph of f, find limit (9,10,11,12,13,14,15,16)
• H11: Given formula for f, find limit (17,19,21,23,41,43,45)
• H12: Polynomial End Behavior (27,31,79)
• H13: Limits at Infinity; End Behavior (33,37,39,65,67,68,69)
• H14: Applied: Time Going to Infinity (85,86,88)
• H15: Find all horizontal & vertical asymptotes (51,53,57,61,63)
• H16: Conceptual Questions (73,74,75,76,77,78)

Section 2.3 Continuity

• H17: Skills Warmup: Interval Notation (2,3,7)
• H18: Given graph of f, find limit and continuity behavior (19,20,27)
• H19: Given specified limit and continuity behavior, sketch graph (11,14)
• H20: Given formula for f, where is f continuous? (35,37,69)
• H21: Conceptual Questions (77,78,79,80,81)
• H22: Positive and Negative Behavior of Graphs and Functions (55,85)
• H23: Solving Inequalities (47,49,51,53)

Section 2.4 The Derivative

• H24: Skills Warmup: Compute Slope of Line (1)
• H25: Secant & Tangent Line Slopes (9,11,13,15,45,47,57)
• H26: Computing f' for Polynomial (19,21,27,29,81,89)
• H27: Computing f' for 1/x and sqrt(x) Type Functions (35,37)
• H28: Given graph of f, where does f' exist? (49,50,51,52,53,54)
• H29: Conceptual Questions: (63,64,65,66,68)

Section 2.5 Basic Differentiation Properties

• H30: Skills Warmup: Rewrite as power function (1,2,3,4,5,6,7,8)
• H31: Constant Function Rule and Power Rule (9,11,13,15,17,19)
• H32: Sum Rule, Const Multiple rule, Power rule (35,37,49)
• H33: Rewrite as sum of const x x^p, then differentiate (45,51,53,55,81)
• H34: Tangent Line and Instantaneous Velocity (59,63)
• H35: Conceptual Question (83,84,85,86)
• H36: Applied Problems (89,91,97)

Section 2.7 Marginal Analysis in Business and Economics

• H37: Skills Warmup: Computing Cost (1,2,3)
• H38: Computing Marginal Quantities (9,13,17)
• H39: Applied Problems (33,43,45,47,49,51)

Section 3.1 The Constant e and Continuous Compound Interest

• H40: Skills Warmup: Solving For Specified Variable (3,7)
• H41: Using Table of Values to Investigate Limit (21,23)
• H42: Continuously Compounded Int (11,13,27,29,31,35,37,41)
• H43: Radioactive Decay (43,45)

Section 3.2 Derivatives of Exponential and Logarithmic Functions

• H44: Differentiating Exponential Functions (13,27,53,57)
• H45: Tangent Line and Applied Problems: Exponential (33,67,69,75)
• H46: Skills Warmup: Rewriting Log Expressions (7,8,9,10)
• H47: Differentiating Logarithmic Functions (15,21,43,44,51,55)
• H48: Tangent Line Problems: Logarithmic (31,35)

Section 3.3 Derivatives of Products and Quotients

• H49: Differentiating Products (17,19,21,55)
• H50: Differentiating Quotients (25,31,33,69)
• H51: Trick: Rewrite First to Eliminate Quotient (59,73)
• H52: Tangent Line Problems Involving Quotients (63,65)
• H53: Applied Problems Involving Quotients (93,95,97)

Section 3.4 The Chain Rule

• H54: Power Function Outer Function (21,27,29,33,37,55,67)
• H55: Exponential or Logarithmic Outer Function (25,31,39,40)
• H56: Applied Problems (91,95,97)
• H57: Product Rule then Chain Rule (47,63)

Section 4.1 First Derivative and Graphs

• H58: Graphical Probs (9,11,13,14,19,21,23,25,61,65,79,83)
• H59: Incr and Decr intervals for function given by formula (49,51,53,55)
• H60: Partition numbers, Critical numbers (27,29,31)
• H61: First Derivative Test (17,43,45,85,97)

Section 4.2 Second Derivative and Graphs

• H62: Shapes of graphs (9,13)
• H63: Find Second Derivative (17,19)
• H64: Given formula for f, determine concavity (33,35,37,87,89)
• H65: Graphing (45,49,57,77)

Section 4.5 Absolute Maxima & Minima

• H66: Identifying Absolute Extrema on Graph (9,17)
• H67: Closed Interval Method (26,67)
• H68: Finding Absolute Extrema on Open Interval (43,49,51,53)
• H69: Second Derivative Test (35,37,73,75)

Section 4.6 Optimization

• H70: Single Variable Maximizing Revenue (19,25,27)
• H71: Two Variable Abstract Max Min Problems (9,13,15,17)
• H72: Two Variable Applied Max Min Fence Problems (33,34,35,36)

Section 5.1 Antiderivatives, Indefinite Integrals

• H73: Rewrite function as sum of const x x^p (1,3,5)
• H74: Is one function antiderivative of another? (25,27,28,29,31,33,34,35,36,37,38)
• H75: Graphs of antiderivatives of a function (39,41)
• H76: Basic Indefinite Integrals (9,11,13,17,19,21,23)
• H77: Rewrite integrand then integrate (43,45,47,49,51,53)
• H78: Find particular antiderivative satisfying extra condition (55,61)

Section 5.2 Integration by Substitution

• H79: Review of Chain Rule Derivatives (3,5,7)
• H80: Is one function an antiderivative of another? (51,52,53,55,56,57)
• H81: Basic Substitution Integrals: Power Function Outer Function and No Leftover Constant (11,15,17,19)
• H82: Harder Substitution Integrals: Leftover Constants and General Outer Functions (23,27,29,31,33,41,65,67)
• H83: Application of Substitution Integrals to Total Change Problems (81,85)

Section 5.4 The Definite Integral

• H84: Approximating areas with Sums (7,13,15,17,19,23,61,73)
• H85: Using Properties of Definite Integral (33,41,45,49,51,53)
• H86: Conceptual Problems (55,56)
• Section 5.5 The Fundamental Theorem of Calculus
• H87: Basic Definite Integrals (11,13,15,17,19,21,23,25,27,31)
• H88: Harder Definite Integrals (35,36,38,39,41,45)
• H89: Total Change Problems (69,71,89)
• H90: Average Value of a Function Over an Interval (49,51,55,92)

Section 6.1 Area between Curves

• H91: Area between curve and x-axis (9,11,17,21,23,25,57)
• H92: Area between two curves (3,5,37,47,53,55,63)
• H93: Applications of the Area Between Two Curves (83,85,89)
• Section 6.2 Applications in Business and Economics
• H94: Total Income from a Continuous Income Stream (37,39,41,43)
• H95: Future Value of Continuous Income Stream (9,13,45,47,49,51,53,67)
• H96: Consumers' Surplus; Consumers' Surplus (69,71,73,75,77)