Nicholas Barvinok

University of Michigan - Ann Arbor

Biography

Nicholas has not yet added a biography.

Education

BS Mathematics
University of Michigan - Ann Arbor
Phd Mathematics
Georgia Institute of Technology - Main Campus

Educator Statistics

Numerade tutor for 7 years
224 Students Helped

Topics Covered

Exploring the World of Derivatives: A Comprehensive Guide
Stand Out with Differentiation Strategies | Boost Your Business
Unlock the Power of Vectors: Discover Their Limitless Possibilities
Unlocking the Power of Functions: Boost Your Programming Skills
Differential Equations Made Simple: Expert Tips & Resources
Power Series
Powers and Polynomial

Nicholas's Textbook Answer Videos

01:23
Biocalculus Calculus for the Life Sciences

Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

$$\begin{array}{ll}{\text { (a) } y=\pi^{x}} & {\text { (b) } y=x^{\pi}} \\ {\text { (c) } y=x^{2}\left(2-x^{3}\right)} & {\text { (d) } y=\tan t-\cos t} \\ {\text { (e) } y=\frac{s}{1+s}} & {\text { (f) } y=\frac{\sqrt{x^{3}-1}}{1+\sqrt[3]{x}}}\end{array}$$

Chapter 1: Functions and Sequences
Section 2: A Catalog of Essential Functions
Nicholas Barvinok
01:07
Biocalculus Calculus for the Life Sciences

Match each equation with its graph. Explain your choices.(Don't use a computer or graphing calculator.)

$\begin{array}{ll}{\text { (a) } y=3 x} & {\text { (b) } y=3^{x}} \\ {\text { (c) } y=x^{3}} & {\text { (d) } y=\sqrt[3]{x}}\end{array}$

Chapter 1: Functions and Sequences
Section 2: A Catalog of Essential Functions
Nicholas Barvinok
01:28
Biocalculus Calculus for the Life Sciences

What do all members of the family of linear functions
$f(x)=1+m(x+3)$ have in common? Sketch several
members of the family.

Chapter 1: Functions and Sequences
Section 2: A Catalog of Essential Functions
Nicholas Barvinok
03:00
Biocalculus Calculus for the Life Sciences

Find expressions for the quadratic functions whose graphs
are shown.

Chapter 1: Functions and Sequences
Section 2: A Catalog of Essential Functions
Nicholas Barvinok
00:49
Biocalculus Calculus for the Life Sciences

Climate change Recent studies indicate that the average surface temperature of the earth has been rising steadily. Some scientists have modeled the temperature by the linear function $T=0.02 t+8.50,$ where $T$ is temperature in $^{\circ} \mathrm{C}$ and $t$ represents years since $1900 .$
(a) What do the slope and $T$ -intercept represent?
(b) Use the equation to predict the average global surface
temperature in 2100 .

Chapter 1: Functions and Sequences
Section 2: A Catalog of Essential Functions
Nicholas Barvinok
00:57
Biocalculus Calculus for the Life Sciences

At the surface of the ocean, the water pressure is the same as the air pressure above the water, 15 $\mathrm{lb} / \mathrm{in}^{2} .$ Below the surface, the water pressure increases by 4.34 $\mathrm{lb} / \mathrm{in}^{2}$ for every 10 $\mathrm{ft}$ of descent.
(a) Express the water pressure as a function of the depth below the ocean surface.
(b) At what depth is the pressure 100 $\mathrm{lb} / \mathrm{in}^{2} ?$

Chapter 1: Functions and Sequences
Section 2: A Catalog of Essential Functions
Nicholas Barvinok
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