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Calculus

Unit 1

Unit 1: Differentiation

Introduction to Differentiation Derivatives Visualizing Differentiation

Unit 2

Unit 2: Integration

Introduction to Integration Integrals Visualizing Integration

Unit 3

Unit 3: Multivariable

Introduction to Multivariable Calculus Multivariable Functions Visualizing Multivariable Calculus

Unit 3 • Chapter 2

Multivariable Functions

Video Summary

This video is a tutorial on how to evaluate limits using the limit properties. The speaker first goes over the three limit properties and then shows how to apply them to solve three practice problems. The key takeaway is to rewrite the limit expressions using proper limit notation.

Knowledge Check

What is a limit of a function?

the value that a function approaches as the input approaches a particular value

a transform that converts a function into a form that describes the frequencies present in the original function

infinite sum of terms that approximate a function as a polynomial

mathematical function that can be formally defined as an improper Riemann integral

What is the multiplicative limit property?

the limit of the product of two functions is equal to the product of the limits of the individual functions

the limit of a function as x approaches a is equal to the limit of the function as x approaches b

the limit of a function as x approaches infinity is equal to the limit of the function as x approaches negative infinity

the limit of a function as x approaches c is equal to the value of the function at c

What is the difference between a limit and a function?

a limit is a value that a function approaches as the input approaches a particular value, while a function is a relation between an input and an output

a limit is a transform that converts a function into a form that describes the frequencies present in the original function, while a function is a mathematical function that can be formally defined as an improper Riemann integral

a limit is an infinite sum of terms that approximate a function as a polynomial, while a function is a certain kind of approximation of an integral by a finite sum

a limit is a mathematical function that can be formally defined as an improper Riemann integral, while a function is a transform that converts a function into a form that describes the frequencies present in the original function

Calculus

Multivariable Functions

Video Summary

Knowledge Check

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Visualizing Multivariable Calculus

Introduction to Multivariable Calculus