Interactive Study Problems for Calculus I

The problems are listed by topic. Section numbers refer to the textbook Calculus from Graphical, Numerical, and Symbolic Points of View by Arnold Ostebee and Paul Zorn. While we no longer use this text here at OU, the problems remain VERY relevant for Calculus I students.

Sample Problems

Section 1.1

Functions, calculus style

Section 1.2

Graphs

Section 1.3

Machine graphics

Section 1.4

What is a function?

Section 1.5

A field guide to elementary functions

Section 2.1

Amount functions and rate functions

Section 2.2

Estimating derivatives

Section 2.3

The geometry of derivatives

Section 2.4

The geometry of higher order derivatives

Section 2.5

Average and instantaneous rates

Section 2.6

Limits and continuity

Section 2.7

Limits involving infinity

Section 2.8

Power functions, polynomials and their derivatives

Section 2.9

Derivatives of exponential and logarithmic functions

Section 2.10

Derivatives of trigonometric functions

Section 3.1

Composition of functions

Section 3.2

Operations with constants and derivatives

Section 3.3

The product and quotient rule

Section 3.4

The Chain Rule

Section 3.5

Implicit Differentiation

Section 3.6

Inverse Trigonometric Functions

Section 3.7

Why continuity matters

Section 3.8

Why differentiability matters

Section 3.9

Optimization and the derivative

Sections 4.1 and 4.2

Differential equations

Section 4.3

Taylor polynomials

Section 4.4

Newton's method

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