Calculus I Midterm: Exam Questions – Week 4, Week 4

Summary

Calculus I is a branch of mathematics. Students learn to find limits, domains and continuous intervals of functions. They also solve equations and express logarithms in different forms.

Finding limits

Limits of functions are found as x approaches a number or infinity. Students find limits of rational functions by dividing by the highest power of x. They find limits of other functions too.

Finding domains and continuity

Students find the domain of a function. They find intervals on which a function is continuous. They do this for functions with different forms.

Expressing logarithms

Logarithms are expressed as a sum and/or difference. Powers are expressed as factors. Students do this for logarithms with different bases and arguments.

Solving equations

Students solve equations. They solve equations with different forms. They solve equations with different bases and arguments.

Key terms

limits

The value that a function approaches as the input approaches a certain value.

domain

The set of all possible inputs for a function.

continuous

A function is continuous if it has no breaks or jumps in its graph.

logarithms

The logarithm of a number is the exponent to which a base must be raised to produce that number.

rational functions

A rational function is a function that can be written as the ratio of two polynomials.

intervals

A set of real numbers with no gaps; a continuous stretch of numbers.

Questions this document helps with

• What is the limit of a function as x approaches a number?
• How do you find the domain of a function?
• How do you express logarithms as a sum and/or difference?

Summary written with AI from the document's text.