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Michael Jacobsen

Idaho State University

Biography

I began teaching at Idaho State University as a teaching assistant in 2010. In 2012 I graduated from ISU and began teaching full time. I greatly enjoy talking about mathematics and statistics in group settings and in tutoring sessions.

Education

MS Mathematics
Idaho State University

Topics Covered

Vectors
Differential Equations
Functions
Introduction to Trigonometry
Applications of Trigonometric Functions
Graphing Trigonometry Functions
Introduction to Conic Sections
Quadratic Functions
Systems of Equations and Inequalities
Sampling and Data
Descriptive Statistics
Introduction to Sequences and Series
Introduction to Combinatorics and Probability
Integration
Integration Techniques
Polynomials
Rational Functions
Sequences
Series
Linear Equations and Inequalities
Equations and Inequalities
Write Linear Equations
Linear Equations and Functions
Functions
Exponential and Logarithmic Functions
Introduction to Matrices
Complex Numbers
Quadratic Equations
Introduction to Algebra
Graph Linear Functions
Derivatives
Differentiation
Parametric Equations
Polar Coordinates

Michael's Textbook Answer Videos

02:02
Thomas Calculus

Each of Exercises $1-4$ gives a value of sinh $x$ or cosh $x$ . Use the definitions and the identity cosh $^{2} x-\sinh ^{2} x=1$ to find the values of the remaining five hyperbolic functions.
$$\sin x=-\frac{3}{4}$$

Chapter 7: Transcendental Functions
Section 7: Hyperbolic Functions
Michael Jacobsen
09:54
Thomas Calculus

Prove the identities
$\begin{aligned} \sinh (x+y) &=\sinh x \cosh y+\cosh x \sinh y \\ \cosh (x+y) &=\cosh x \cosh y+\sinh x \sinh y \end{aligned}$
Then use them to show that
a. \sinh 2 x=2 \sinh x \cosh x
b. \cosh 2 x=\cosh ^{2} x+\sinh ^{2} x

Chapter 7: Transcendental Functions
Section 7: Hyperbolic Functions
Michael Jacobsen
03:21
Thomas Calculus

Which of the following functions grow faster than $e^{x}$ as $x \rightarrow \infty ?$ Which grow at the same rate as $e^{x} ?$ Which grow slower?
a. $x-3 \quad$ b. $x^{3}+\sin ^{2} x$
c. $\sqrt{x} \quad$ d. $4^{x}$
e. $(3 / 2)^{x} \quad$ f. $e^{x / 2}$
g. $e^{x} / 2 \quad$ h. $\log _{10} x$

Chapter 7: Transcendental Functions
Section 8: Relative Rates of Growth
Michael Jacobsen
05:09
Thomas Calculus

Which of the following functions grow faster than $e^{x}$ as $x \rightarrow \infty ?$ Which grow at the same rate as $e^{x} ?$ Which grow slower?
a. $10 x^{4}+30 x+1 \quad$ b. $x \ln x-x$
c. $\sqrt{1+x^{4}}$ d. $(5 / 2)^{x}$
e. $e^{-x} \quad$ f. $x e^{x}$
g. $e^{\cos x}$ h. $e^{x-1}$

Chapter 7: Transcendental Functions
Section 8: Relative Rates of Growth
Michael Jacobsen
07:41
Thomas Calculus

Which of the following functions grow faster than $x^{2}$ as $x \rightarrow \infty$ ? Which grow at the same rate as $x^{2}$ ? Which grow slower?
a. $x^{2}+4 x$ b. $x^{5}-x^{2}$
c. $\sqrt{x^{4}+x^{3}} \quad$ d. $(x+3)^{2}$
g. $x^{3} e^{-x}$ h. 8$x^{2}$

Chapter 7: Transcendental Functions
Section 8: Relative Rates of Growth
Michael Jacobsen
03:04
Thomas Calculus

In Exercises $13-24,$ find the derivative of $y$ with respect to the appropriate variable.
$$y=\left(x^{2}+1\right) \operatorname{sech}(\ln x)$$

Chapter 7: Transcendental Functions
Section 7: Hyperbolic Functions
Michael Jacobsen
1 2 3 4 5 ... 195

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