# Aktuelle oppgaver

Alle oppgaver oppgitt under er hentet fra Adams og Essex: ’Calculus: A complete course’, 8. utgave.

## Grenser og kontinuitet

Kapittel 1.1: Examples of Velocity, Growth Rate, and Area
1.1.5-8, 1.1.12-13.

Kapittel 1.2: Limits of Functions
1.2.1, 1.2.3, 1.2.5, 1.2.9, 1.2.23, 1.2.25, 1.2.55, 1.2.57, 1.2.75 , 1.2.77.

Kapittel 1.3: Limits at Infinity and Infinite Limits
1.3.3, 1.3.13, 1.3.29, 1.3.33.

Kapittel 1.4: Continuity
1.4.1, 1.4.3, 1.4.5 ,1.4.11, 1.4.15, 1.4.17, 1.4.23, 1.4.29, 1.4.31.

Kapittel 1.5: The Formal Definition of Limit
1.5.1, 1.5.5, 1.5.9, 1.5.20.

## Derivasjon

Kapittel 2.1: Tangent Lines and Their Slopes
2.1.1, 2.1.11, 2.1.16, 2.1.23.

Kapittel 2.2: The Derivative
2.2.3, 2.2.19, 2.2.48, 2.2.55.

Kapittel 2.3: Differentiation Rules
2.3.7, 2.3.29, 2.3.31, 2.3.46.

Kapittel 2.4: The Chain Rule
2.4.5, 2.4.13, 2.4.24, 2.4.27.

Kapittel 2.5: Derivatives of Trigonometric Functions
2.5.16, 2.5.35, 2.5.53, 2.5.58.

Kapittel 2.6: Higher Order Derivatives
2.6.15.

Kapittel 2.7: Using Differentials and Derivatives
2.7.12, 2.7.21, 2.7.23.

Kapittel2.8: The Mean Value Theorem
2.8.4, 2.8.15, 2.8.21.

Kapittel 2.9: Implicit Differentiation
2.9.5, 2.9.16, 2.9.17.

Kapittel 2.10: Antiderivatives and Initial-Value Problems
2.10.12, 2.10.26, 2.10.42.

Kapittel 2.11: Velocity and Acceleration
2.11.7, 2.11.12.

## Transcendentale funksjoner

Kapittel 3.1: Inverse Functions
3.1.3, 3.1.7, 3.1.11, 3.1.21, 3.1.25, 3.1.28, 3.1.34.

Kapittel 3.2: Exponential and Logarithmic Functions
3.2.3, 3.2.5, 3.2.15, 3.2.26, 3.2.31.

Kapittel 3.3: The Natural Logarithm and Exponential
3.3.3, 3.3.7, 3.3.15, 3.3.17, 3.3.39, 3.3.45, 3.3.54, 3.3.60.

Kapittel 3.4: Growth and Decay
3.4.1, 3.4.3, 3.4.7, 3.4.11, 3.4.12.

Kapittel 3.5: The Inverse Trigonometric Functions
3.5.11, 3.5.17, 3.5.19, 3.5.29, 3.5.33, 3.5.43.

Kapittel 3.6: Hyperbolic Functions
3.6.2, 3.6.5, 3.6.7, 3.6.9.

## Anvendelser av derivasjon

Kapittel 4.1: Related rates
4.1.1, 4.1.3, 4.1.6, 4.1.18.

Kapittel 4.2: Finding roots of equations
4.2.1, 4.2.3, 4.2.8, 4.2.11.

Kapittel 4.3: Indeterminate forms
4.3.1, 4.3.3, 4.3.12, 4.3.23, 4.3.26, 4.3.32.

Kapittel 4.4: Extreme values
4.4.1, 4.4.3, 4.4.6, 4.4.9, 4.4.19, 4.4.25, 4.4.32.

Kapittel 4.5: Concavity and inflections
4.5.1, 4.5.3, 4.5.4, 4.5.17, 4.5.28, 4.5.35.

Kapittel 4.6: Sketching the graph of a function
4.6.7, 4.6.11, 4.6.16, 4.6.23.

Kapittel 4.7: Graphing with computers
-

Kapittel 4.8: Extreme-value problems
4.8.1, 4.8.2, 4.8.13, 4.8.28, 4.8.31, 4.8.39, 4.8.49.

Kapittel 4.9: Linear approximations
4.9.1, 4.9.3, 4.9.10, 4.9.29.

Kapittel 4.10: Taylor polynomials
4.10.1, 4.10.6, 4.10.9, 4.10.10, 4.10.22, 4.10.27, 4.10.28.

Kapittel 4.11: Roundoff error, truncation error, and computers
-

## Integrasjon

Kapittel 5.1: Sums and Sigma Notation
5.1.1, 5.1.3, 5.1.7, 5.1.9, 5.1.11, 5.1.16, 5.1.17, 5.1.21, 5.1.24, 5.1.32.

Kapittel 5.2: Areas as Limits of Sums
5.2.3, 5.2.12, 5.2.19.

Følgende Maple-regneark kan være nyttig her: Summer og Riemannsummer

Kapittel 5.3: The Definite Integral
5.3.1, 5.3.2, 5.3.9 (det kan lønne seg å bruke resultatet fra oppgave 5.1.39 i oppgave 5.3.9).

Kapittel 5.4: Properties of the Definite Integral
5.4.1, 5.4.7, 5.4.9, 5.4.23, 5.4.27, 5.4.33, 5.4.42.

Kapittel 5.5: The Fundamental Theorem of Calculus
5.5.1, 5.5.6, 5.5.7, 5.5.11, 5.5.14, 5.5.23, 5.5.33, 5.5.39,41, 5.5.44, 5.5.49.

Kapittel 5.6: The Method of Substitution
5.6.1, 5.6.2, 5.6.5, 5.6.7, 5.6.8, 5.6.12, 5.6.21, 5.6.22, 5.6.45.

Følgende Maple-regneark kan være nyttig her: Substitutions

Kapittel 5.7: Areas of Plane Regions
5.7.1, 5.7.6, 5.7.29.

## Integrasjonsteknikker

Kapittel 6.1: Integration by Parts
6.1.1, 6.1.4, 6.1.13, 6.1.33, 6.1.37.

Relevant Mapleark: Partial integration

Kapittel 6.2: Integrals of Rational Functions
6.2.1, 6.2.3, 6.2.7, 6.2.9, 6.2.20, 6.2.27.

Relevant Mapleark: Rational Functions

Kapittel 6.3: Inverse Substitutions
6.3.1, 6.3.8, 6.3.43, 6.3.46, 6.3.49, 6.3.51.

Relevant Mapleark : Substitutions

Kapittel 6.4: Other Methods for Evaluating Integrals
6.4.1, 6.4.3.

Relevant pencast: The method of undetermined coefficients

Kapittel 6.5: Improper Integrals
6.5.1, 6.5.3, 6.5.5, 6.5.6, 6.5.27, 6.5.31.

Kapittel 6.6: The Trapezoid and Midpoint Rules
6.6.1, 6.6.5.

Kapittel 6.7: Simpson's Rule
6.7.1, 6.7.5.

Relevant Mapleark: Numerical Integration

Kapittel 6.8: Other Aspects of Approximate Integration
6.8.1, 6.8.7, 6.8.9, 6.8.10.

## Anvendelser av integrasjon

Kapittel 7.1: Volumes by Slicing – Solids of Revolution
7.1.1, 7.1.5, 7.1.7, 7.1.11, 7.1.18.

Følgende Maple-regneark kan være nyttig her: Rotasjonslegemer

Kapittel 7.2: More Volumes by Slicing
7.2.1, 7.2.15.

Kapittel 7.3: Arc Length and Surface Area
7.3.1, 7.3.7, 7.3.15, 7.3.23, 7.3.24, 7.3.34, 7.3.37.

Følgende Maple-regneark kan være nyttig her: Buelengde

Kapittel 7.4: Mass, Moments, and Centre of Mass
7.4.1, 7.4.2, 7.4.3, 7.4.4, 7.4.16.

Følgende Maple-regneark kan være nyttig her: Massesenter

Section 7.5: Centroids
7.5.1,2, 7.5.15, 7.5.23.

Section 7.6: Other Physical Applications
7.6.1, 7.6.3, 7.6.6.

## Differensialligninger

Kapittel 7.9: First-Order Differential Equations
7.9.1, 7.9.6, 7.9.7, 7.9.11, 7.9.13, 7.9.19, 7.9.21, 7.9.28, 7.9.31.

Kapittel 18.1: Classifying Differential Equations
18.1.1, 18.1.3.

Kapittel 18.3: Existence, Uniqueness, and Numerical Methods
18.3.1-3, 18.3.4-6, 18.3.13, 18.3.15, 18.3.16.

Følgende Maple-regneark kan være nyttig her: Numeriske metoder

## Følger, rekker og potensrekker

Kapittel 9.1: Sequences and Convergence
9.1.1, 9.1.3, 9.1.24, 9.1.31, 9.1.34, 9.1.36.

Kapittel 9.2: Infinite Series
9.2.1, 9.2.10, 9.2.11, 9.2.16, 9.2.19, 9.2.21.

Kapittel 9.3: Convergence Tests for Positive Series
9.3.1, 9.3.4, 9.3.7, 9.3.9, 9.3.18, 9.3.28, 9.3.38.

Følgende Maple-regneark kan være nyttige her:
Konvergenstester
Gjennomgang av oppgave 9.3.28

Kapittel 9.4: Absolute and Conditional Convergence
9.4.1, 9.4.5, 9.4.13, 9.4.20.

Kapittel 9.5: Power Series
9.5.1, 9.5.5, 9.5.12, 9.5.13, 9.5.15, 9.5.21.

Følgende Maple-regneark kan være nyttige her:
Potensrekker
Gjennomgang av oppgave 9.5.12

Kapittel 9.6: Taylor and Maclaurin Series
9.6.1, 9.6.2, 9.6.7, 9.6.29, 9.6.37.

Kapittel 9.7: Applications of Taylor and Maclaurin Series
9.7.1, 9.7.15, 9.7.21, 9.7.24.