Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Textbooks
Test Prep
Numerade for Schools
Courses
Class
Ask Question
StudyParty
Earn Money
Refer a friend. Get $50! Become an Educator

Log in

Yuki Hotta

California State University - Long Beach

Biography

Through college I've been tutoring my peers and after graduating University of California, Berkeley with a BA in math in 2009 I've been teaching math to students. Currently pursuing my MS in Statistics at California State University, Long Beach.

https://www.linkedin.com/in/yuki-hotta-895668203/

Education

MS Statistics

California State University - Long Beach

BA Mathematics

University of California, Berkeley

Topics Covered

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Integrals

Applications of Integration

Differentiation

Derivatives

Applications of the Derivative

Integration Techniques

Limits

Polar Coordinates

Vectors

Lines and Planes in Space

Functions

Integration

Trigonometry

An Introduction to Geometry

Equations and Inequalities

Continuous Functions

Geometry Basics

Functions

Linear Functions

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

Volume

Yuki's Textbook Answer Videos

Each integral represents the volume of a solid. Describe the solid.

$ \pi \displaystyle \int_{-1}^1 (1 -y^2)^2 dy $

Chapter 6: Applications of Integration

Section 2: Volumes

A formula for the derivative of a function $f$ is given. How many critical numbers does $f$ have?

$ f'(x) = 5e^{-0.1 |x|} \sin x - 1 $

Chapter 4: Applications of Differentiation

Section 1: Maximum and Minimum Values

Find the absolute maximum and absolute minimum values of $f$ on the given interval.

$ f(x) = \frac{x}{x^2 - x + 1} $, $ [0, 3] $

Chapter 4: Applications of Differentiation

Section 1: Maximum and Minimum Values

(a) Use a graph to estimate the absolute maximum and minimum values of the function to two decimal places.
(b) Use calculus to find the exact maximum and minimum values.

$ f(x) = x^5 - x^3 + 2 $, $ -1 \leqslant x \leqslant 1 $

Chapter 4: Applications of Differentiation

Section 1: Maximum and Minimum Values

Show that $5$ is a critical number of the function
$$ g(x) = 2 + (x - 5)^3 $$
but $g$ does not have a local extreme value at $5$.

Chapter 4: Applications of Differentiation

Section 1: Maximum and Minimum Values

With a programmable calculator or computer (see the instructions for Exercise 5.1.9), compute the left and right Riemann sums for the function $ f(x) = x/(x + 1) $ on the interval $ [0, 2] $ with $ n = 100 $. Explain why these estimates show that $$ 0.8946 < \int^2_0 \frac{x}{x + 1} \, dx < 0.9081 $$

Chapter 5: Integrals

Section 2: The Definite Integral

1 2 3 4 5 ... 24

About

Our Story
Careers
Our Educators
Numerade Blog

Browse

Courses
Books
Topics
Test Prep
Ask Directory

Support

Help
Privacy Policy
Terms of Service
FAQ

Get started