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0. Functions
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Chapter worksheet
Introduction to Functions
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Piecewise Functions
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Properties of Functions
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Common Functions
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Transformations
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Combining Functions
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Exponent Rules
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Exponential Functions
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Logarithmic Functions
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Properties of Logarithms
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Exponential & Logarithmic Equations
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1. Limits and Continuity
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Chapter worksheet
Introduction to Limits
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Finding Limits Algebraically
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Continuity
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2. Intro to Derivatives
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Chapter worksheet
Tangent Lines and Derivatives
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Derivatives as Functions
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Basic Graphing of the Derivative
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Differentiability
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3. Techniques of Differentiation
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Chapter worksheet
Basic Rules of Differentiation
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Higher Order Derivatives
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Product and Quotient Rules
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The Chain Rule
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4. Derivatives of Exponential & Logarithmic Functions
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Chapter worksheet
Derivatives of Exponential & Logarithmic Functions
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5. Applications of Derivatives
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Chapter worksheet
Implicit Differentiation
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Logarithmic Differentiation
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Related Rates
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Differentials
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Linearization
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6. Graphical Applications of Derivatives
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Chapter worksheet
Intro to Extrema
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The First Derivative Test
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Concavity
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The Second Derivative Test
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Curve Sketching
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Finding Global Extrema
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Applied Optimization
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7. Antiderivatives & Indefinite Integrals
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Chapter worksheet
Antiderivatives
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Indefinite Integrals
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8. Definite Integrals
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Chapter worksheet
Estimating Area with Finite Sums
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Riemann Sums
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Introduction to Definite Integrals
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Fundamental Theorem of Calculus
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Average Value of a Function
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Substitution for Indefinite Integrals
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Substitution for Definite Integrals
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9. Graphical Applications of Integrals
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Chapter worksheet
Area Between Curves
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Introduction to Volume & Disk Method
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10. Integrals of Inverse, Exponential, & Logarithmic Functions
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Chapter worksheet
Integrals of Exponential Functions
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Integrals Involving Logarithmic Functions
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11. Techniques of Integration
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Chapter worksheet
Integration by Parts
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Improper Integrals
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12. Trigonometric Functions
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Chapter worksheet
Angles
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Trigonometric Functions on Right Triangles
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Solving Right Triangles
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Trigonometric Functions on the Unit Circle
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Graphs of Sine & Cosine
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Graphs of Other Trigonometric Functions
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Trigonometric Identities
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Derivatives of Trig Functions
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Integrals of Basic Trig Functions
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Integrals of Other Trig Functions
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13: Intro to Differential Equations
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Chapter worksheet
Basics of Differential Equations
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Slope Fields
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Separable Differential Equations
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14. Sequences & Series
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Chapter worksheet
Sequences
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Review of Factorials
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Series
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15. Power Series
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Chapter worksheet
Power Series & Taylor Series
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16. Probability & Calculus
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Chapter worksheet
Continuous Probability Models
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16. Probability & Calculus
Continuous Probability Models
16. Probability & Calculus
Continuous Probability Models: Videos & Practice Problems
Video Lessons
Practice
Worksheet
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Problem 16
Multiple Choice
A climatologist models April daily average temperature T (in °F) as having PDF f(t) = k(t - 60) for 60 ≤ t ≤ 90 and f(t)=0 otherwise. (a) Find k. (b) Using that model, compute the probability temperature falls between 75°F and 81°F.
A
(a) k = 1/300; (b) 0.30 because the integrator used an incorrect squared term when normalizing
B
(a) k = 1/450; (b) 0.48 because the student accidentally doubled the computed area for the interval 75–81
C
(a) k = 1/450; (b) 0.24
D
(a) k = 1/450; (b) 0.216 because the final division by 900 was mistakenly replaced by division by 1000
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