Jimmy Yao

University of California, Berkeley
Graduate Student Instructor

Biography

I taught 128A: Numeric analysis at UC Berkeley.

Education

Phd Math
University of California, Berkeley

Educator Statistics

Numerade tutor for 6 years
332 Students Helped

Topics Covered

Mastering Equations and Inequalities: Your Guide to Mathematical Success
Functions
Mastering Linear Functions: A Comprehensive Guide
Integration
Mastering Integration Techniques for Optimal Results
Applications of Integration: Exploring Real-World Solutions
Discover the Best Series to Binge-Watch | Your Ultimate Guide
Unlock the Power of Vectors: Discover Their Limitless Possibilities
Master Vector Calculus with Our Comprehensive Guide
Exploring the World of Derivatives: A Comprehensive Guide
Stand Out with Differentiation Strategies | Boost Your Business
Breaking Limits: Unlock Your Potential with Our Expert Solutions
Mastering Integrals: Tips and Tricks for Calculus Success
Mastering Partial Derivatives: Essential Techniques and Tips
Exploring the Functions of Multiple Variables
Unlocking the Power of Functions: Boost Your Programming Skills
Mastering the Basics of Parametric Equations: A Comprehensive Guide
Polar Coordinates: Understanding the Basics and Applications

Jimmy's Textbook Answer Videos

04:00
Calculus: Early Transcendentals

(a) Show that the absolute value function $ F(x) = | x | $ is continuous everywhere.
(b) Prove that if $ f $ is a continuous function on an interval, then so is $ | f | $.
(c) Is the converse of the statement in part (b) also true? In other words, if $ | f | $ is continuous, does it follow that $ f $ is continuous? If so, prove it. If not, find a counterexample.

Chapter 2: Limits and Derivatives
Section 5: Continuity
Jimmy Yao
02:35
Calculus: Early Transcendentals

Verify that the conclusion of Clairaut's Theorem holds, that is, $ u_{xy} = u_{yx} $.
$ u = x^4y^3 - y^4 $

Chapter 14: Partial Derivatives
Section 3: Partial Derivatives
Jimmy Yao
04:41
Calculus: Early Transcendentals

Find the minimum value of $ f(x, y, z) = x^2 + 2y^2 + 3z^2 $ subject to the constraint $ x + 2y + 3z = 10 $. Show that $ f $ has no maximum value with this constraint.

Chapter 14: Partial Derivatives
Section 8: Lagrange Multipliers
Jimmy Yao
03:37
Calculus: Early Transcendentals

Find the gradient vector field of $ f $.

$ f(x, y, z) = x^2 y e^{y/z} $

Chapter 16: Vector Calculus
Section 1: Vector Fields
Jimmy Yao
04:17
Calculus: Early Transcendentals

Find the slope of the tangent line to the given polar curve at the point specified by the value of $ \theta $.
$ r = 2\cos\theta $, $ \quad \theta = \pi/3 $

Chapter 10: Parametric Equations and Polar Coordinates
Section 3: Polar Coordinates
Jimmy Yao
02:00
Calculus of a Single Variable

Disk Method Explain how to use the disk method to
find the volume of a solid of revolution.

Chapter 7: Applications of Integration
Section 2: Volume: The Disk Method
Jimmy Yao
1 2 3 4 5 ... 52

Jimmy's Quick Ask Videos

08:48
Intro Stats / AP Statistics

Find the z-score corresponding to the given area. Remember, z is distributed as the standard normal distribution with mean of and standard deviation .
a.) The area to the left of z is 15%.
b.) The area to the right of z is 65%.
c.) The area to the left of z is 10%.
d.) The area to the right of z is 5%.
e.) The area between and z is 95%. (Hint draw a picture and figure out the area to the left of the .)
f.) The area between and z is 99%.

Jimmy Yao
03:19
Calculus 2 / BC

What is the answer?

Jimmy Yao
04:00
Calculus 1 / AB

(a) Show that the absolute value function $ F(x) = | x | $ is continuous everywhere.
(b) Prove that if $ f $ is a continuous function on an interval, then so is $ | f | $.
(c) Is the converse of the statement in part (b) also true? In other words, if $ | f | $ is continuous, does it follow that $ f $ is continuous? If so, prove it. If not, find a counterexample.

Jimmy Yao
06:08
Calculus 1 / AB

[T] The velocity $V$ (in centimeters per second) of blood in an artery at a distance $x \mathrm{cm}$ from the center of the artery can be modeled by the function
$$
V=f(x)=500\left(0.04-x^{2}\right) \text { for } 0 \leq x \leq 0.2
$$
a. Find $x=f^{-1}(V)$
b. Interpret what the inverse function is used for.
c. Find the distance from the center of an artery with
a velocity of $15 \mathrm{cm} / \mathrm{sec}, 10 \mathrm{cm} / \mathrm{sec}$ , and 5 $\mathrm{cm} / \mathrm{sec}$ .

Jimmy Yao
05:20
Calculus 1 / AB

[T] The cost to remove a toxin from a lake is modeled by the function $C(p)=75 p /(85-p),$ where $C$ is the cost (in thousands of dollars) and $p$ is the amount of toxin in a small lake (measured in parts per billion [ppbl). This model is valid only when the amount of toxin is less than 85 $\mathrm{ppb}$ .
a. Find the cost to remove $25 \mathrm{ppb}, 40 \mathrm{ppb},$ and 50 $\mathrm{ppb}$
of the toxin from the lake.
b. Find the inverse function. c. Use part b. to determine how much of the toxin is removed for
$\$ 50,000$ .

Jimmy Yao
02:44
Calculus 1 / AB

For the following exercises, the position function of a ball dropped from the top of a 200 -meter tall building is given by $s(t)=200-4.9 t^{2},$ where position $s$ is measured in meters and time $t$ is measured in seconds. Round your answer to eight significant digits.
[T] Compute the average velocity of the ball over the given time intervals.
a. $[4.99,5]$
b. $[5,5.01]$
C. $[4.999,5]$
d. $[5,5.001]$

Jimmy Yao
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