Christopher Mark

Numerade Educator
Tutor

Biography

My name is Chris Smith. I am a graduate of Virginia Tech where I earned my Masters in Dynamics and Control of Aerospace Vehicles in 2011. In 2009 I received my Bachelors in Aerospace Engineering from Virginia Tech. My teaching subjects are: math, physics, computer science, engineering, and engineering. Currently, I am a Systems Engineer working on Satellites. I have had about 10 years of professional engineering experience.
A fun fact about me is, I have been involved in over 30 rocket launches while working with NASA. Currently, I am a Systems Engineer working on Satellites. With teaching I have a very adaptable and practical approach. I see each student and lesson as a unique learning opportunity. I seek to help students understand more than just the computations or principles of what they are studying. I want them to know how it all connects to a bigger picture and the really cool things that they can do with science, engineering, math, and just about anything. A lot of the time, I find that the complex subject matters can be broken down into bite sized chunks that make learning manageable and fun.

Education

Christopher has not yet added their education credentials.

Educator Statistics

Numerade tutor for 6 years
96 Students Helped

Topics Covered

Unlock the Power of Vectors: Discover Their Limitless Possibilities
Vector Functions: Understanding the Basics
Breaking Limits: Unlock Your Potential with Our Expert Solutions

Christopher's Textbook Answer Videos

02:56
Thomas Calculus

Length of helix The length 2$\pi \sqrt{2}$ of the turn of the helix in
Example 1 is also the length of the diagonal of a square 2$\pi$ units
on a side. Show how to obtain this square by cutting away and
flattening a portion of the cylinder around which the helix winds.

Chapter 13: Vector-Valued Functions and Motion in Space
Section 3: Arc Length in Space
Christopher Mark
02:30
Calculus of a Single Variable

In Exercises $1-6,$ use the graph to determine the limit, and discuss the continuity of the function.
$$
\begin{array}{lll}{\text { (a) } \lim _{x \rightarrow c^{+}} f(x)} & {\text { (b) } \lim _{x \rightarrow c^{-}} f(x)} & {\text { (c) } \lim _{x \rightarrow c} f(x)}\end{array}
$$
Graph cannot copy.

Chapter 1: Limits and Their Properties
Section 4: Continuity and One-Sided Limits
Christopher Mark
02:16
Calculus of a Single Variable

In Exercises $1-6,$ use the graph to determine the limit, and discuss the continuity of the function.
$$
\begin{array}{lll}{\text { (a) } \lim _{x \rightarrow c^{+}} f(x)} & {\text { (b) } \lim _{x \rightarrow c^{-}} f(x)} & {\text { (c) } \lim _{x \rightarrow c} f(x)}\end{array}
$$
Graph cannot copy.

Chapter 1: Limits and Their Properties
Section 4: Continuity and One-Sided Limits
Christopher Mark
03:05
Calculus of a Single Variable

In Exercises $1-6,$ use the graph to determine the limit, and discuss the continuity of the function.
$$
\begin{array}{lll}{\text { (a) } \lim _{x \rightarrow c^{+}} f(x)} & {\text { (b) } \lim _{x \rightarrow c^{-}} f(x)} & {\text { (c) } \lim _{x \rightarrow c} f(x)}\end{array}
$$
Graph cannot copy.

Chapter 1: Limits and Their Properties
Section 4: Continuity and One-Sided Limits
Christopher Mark
02:47
Calculus of a Single Variable

In Exercises $1-6,$ use the graph to determine the limit, and discuss the continuity of the function.
$$
\begin{array}{lll}{\text { (a) } \lim _{x \rightarrow c^{+}} f(x)} & {\text { (b) } \lim _{x \rightarrow c^{-}} f(x)} & {\text { (c) } \lim _{x \rightarrow c} f(x)}\end{array}
$$
Graph cannot copy.

Chapter 1: Limits and Their Properties
Section 4: Continuity and One-Sided Limits
Christopher Mark
01:54
Calculus of a Single Variable

In Exercises $1-6,$ use the graph to determine the limit, and discuss the continuity of the function.
$$
\begin{array}{lll}{\text { (a) } \lim _{x \rightarrow c^{+}} f(x)} & {\text { (b) } \lim _{x \rightarrow c^{-}} f(x)} & {\text { (c) } \lim _{x \rightarrow c} f(x)}\end{array}
$$
Graph cannot copy.

Chapter 1: Limits and Their Properties
Section 4: Continuity and One-Sided Limits
Christopher Mark
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