The limit of (6x+9)/x^4+6x^3+9x^2 as x approaches -3 does not exist. If you factor the rational expression you get: (6x+9)/[x^4+6x^3+9x^2] = 3(2x+3) / [ (x^2)(x+3)(x+3) ] If we let x go to -3 (from both sides) the numerator...

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as of 10/30/13

Usually responds in about 15 hours

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If you answered “yes” to ANY of the above questions, then you should consider a math tutor. We'll spend an hour or two each week working and playing with math concepts, discussing mathematical principles, and focusing on any uncertainties or difficulties that you are having. There will be an emphasis on having fun, so puzzles and games, and real-world problems, will be used as instruction tools. No homework will be assigned.

Struggling students will improve their grades. Students who are currently “making the grade” will be more confident regarding their abilities and will be fully prepared for “honors” level instruction. High School students will be prepared for pre-calculus and calculus instruction, and will be in position to confidently pass their AP tests.

ALL students are fully capable of high academic achievement. However, many students are not confident in their abilities. It is my goal to increase each student's ability to understand the material and to learn effectively. Mathematics is not "difficult" if it is approached the right way. Anyone with the desire can learn algebra, trigonometry, and calculus if each concept is simplified.

Tutor: Dr. Andrew G.

B.S. Civil Engineering, Carnegie-Mellon University

M.S., Ph.D. Environmental Engineering Science, California Institute of Technology (Caltech)

Dr. G.'s qualifications include a Ph.D. in engineering from CalTech (including a minor in numerical methods/applied math) and over 25 years experience as a practicing environmental engineer/scientist. In addition, he has a lifelong passion for mathematics and, in addition to tutoring all grade levels in math, has volunteered for 6 years in the local public schools in San Rafael (including mathematics instruction and Odyssey of the Mind coach). Dr. G. has a daughter who is currently in high school. He enjoys music, hiking and geocaching.

Andy has worked out very well for our son. He is thoughtful, thorough and patient.

Andrew is a patient and attentive tutor, making sure my son understands the math concepts that he has difficulty with. He gives his full attention to the questions my son has in the areas that he has trouble with, and explains the concepts clearly, so he can grasp them and be able to solve the problems more easily. Great, caring tutor!

Andrew and I sat down and worked on homework problems I was struggling with. He helped give me a better understanding and gave me a solid approach towards problems in the future. Overall Andrew was very clear, patient and made the problems interesting. It's all about relating the sometimes difficult topics to something you understand in the real world. I would definitely recommend Andrew to anyone who needs help in physics.

Math:

Algebra 1, Algebra 2, Calculus, Differential Equations, Discrete Math, Geometry,
Linear Algebra,
Science:

Physics
Homeschool:

Algebra 1, Algebra 2, Calculus, Geometry, Physics, Prealgebra, Precalculus, SAT Math, Statistics
Test Preparation:

SAT Math
Corporate Training:

Statistics
Approved subjects are in **bold**.

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Dr. Andrew G. has a Ph.D. from Caltech in environmental engineering science with a minor in numerical methods. In addition he has over 30 years experience as a practicing atmospheric scientist and dispersion modeler.

The concepts of Linear Algebra are at the heart of (1) numerical methods (used to develop and evaluate solution techniques that are used by computers to solve large numerical systems such as finite element analyses), (2) numerical solutions of overdetermined systems (i.e., "least squares" which are used in atmospheric receptor modeling techniques such as the Chemical Mass Balance model), and (3) statistical models (correlation and multiple regression).

Dr. Gray's research in air pollution includes the use of meteorological and dispersion computer models which involve numerical solutions of large linear (and non-linear) systems. Dr. Gray has also worked with (and helped in the development of) receptor models such as the Chemical Mass Balance Model and other related multivariate factor-analysis techniques. In addition, he has developed computer programs for the efficient (and stable) solution of linear systems (using such methods as Gram-Schmidt orthogonalization).

Topics in Linear Algebra include:

* Systems of Equations and Matrices - Systems of Equations, Row-Echelon Form, Reduced Row-Echelon Form, Gaussian Elimination, Gauss-Jordan Elimination, Matrices, Matrix Arithmetic, Transpose, Inverse Matrices, LU-Decompositions.

* Determinants - The Determinant Function, Properties of Determinants, Method of Cofactors, Determinants by Row Reduction, Cramer's Rule.

* Euclidean N-space - Vectors, Vector Arithmetic, Norm, Dot Product, Cross Product, Projections, Euclidean N-space, Linear Transformations.

* Vector Spaces - Vector Space Axioms, Subspaces, Span, Linear Independence, Linear Dependence, Basis, Dimension, Null Space, Row Space, Column Space, Inner Product Spaces, Orthogonal/Orthonormal Basis, Least Squares, QR-Decomposition, Orthogonal Matrices.

* Eigenvalues and Eigenvectors - Eigenvalues and Eigenvectors, Eigenspaces, Diagonalization, Jordan Canonical Form.

Tutors have the ability to create educational resources and share them with the WyzAnt community. Here are some of the resources created by Andrew. View all of Andrew’s resources

The limit of (6x+9)/x^4+6x^3+9x^2 as x approaches -3 does not exist. If you factor the rational expression you get: (6x+9)/[x^4+6x^3+9x^2] = 3(2x+3) / [ (x^2)(x+3)(x+3) ] If we let x go to -3 (from both sides) the numerator...

find the lim as x goes to 0 (answer)

In this problem, you are actually being asked to derive the derivative of f(x) = 1/x^2 (i.e., 1 over x squared). You are doing this using the formal definition of the derivative, although in algebra class (or precalculus), this is called the "difference quotient"...

Why is the 0 exponent equal 1? (answer)

Think of "multiplication" as always including an extra "1" as a multiplier. (Since 1 is the multiplication identity, the product is never changed by multiplying by 1). When we multiply numbers, we can start with a 1 (identity) and then multiply it by the rest of...

**Very thoughtful, thorough and patient.** —
Andy has worked out very well for our son. He is thoughtful, thorough and patient.
...

Standard Hourly Fee: $55.00

Cancellation: 2 hours notice required

Andrew will travel within 10 miles of San Rafael, CA 94903.

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Andrew G. passed a background check on 10/30/13. The check was ordered by another user through First Advantage. For more information, please review the background check information page.

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