At the moment, I am a Graduate Assistant at LSU. This semester I am teaching College Trigonometry, and in the previous semester, I taught College Algebra. Before that, I worked as a Teaching Assistant at Nazarbayev University. The classes I taught there include: Calculus I, II, and III, Linear Algebra, Precalculus.
$3-10$ Find a power series representation for the function anddetermine the interval of convergence.
$$f(x)=\frac{3}{1-x^{4}}$$
$11-12$ Express the function as the sum of a power series by firstusing partial fractions. Find the interval of convergence.
$$f(x)=\frac{x+2}{2 x^{2}-x-1}$$
(a) Use differentiation to find a power series representationfor$$f(x)=\frac{1}{(1+x)^{2}}$$What is the radius of convergence?(b) Use part (a) to find a power series for$$f(x)=\frac{1}{(1+x)^{3}}$$(c) Use part (b) to find a power series for$$$f(x)=\frac{x^{2}}{(1+x)^{3}}f(x)=\frac{x^{2}}{(1+x)^{3}}$$
(a) Find a power series representation for $f(x)=\ln (1+x)$ .What is the radius of convergence?(b) Use part (a) to find a power series for $f(x)=x \ln (1+x)$(c) Use part (a) to find a power series for $f(x)=\ln \left(x^{2}+1\right)$
$15-18$ Find a power series representation for the function anddetermine the radius of convergence.
$$f(x)=\ln (5-x)$$
Explain why the function is discontinuous at the given number $ a $. Sketch the graph of the function.
$ f(x) = \left\{ \begin{array}{ll} \dfrac{x^2 - x}{x^2 - 1} & \mbox{if $ x \neq 1 $} \hspace{40mm} a = 1\\ 1 & \mbox{if $ x = 1 $} \end{array} \right.$
Consider the following function. f(x) = x + 2 x2(a) Find the critical numbers of f. (Enter your answers as acomma-separated list.) x = (b)Find the open intervals on which the function is increasing ordecreasing. (Enter your answers using interval notation. If ananswer does not exist, enter DNE.) increasing decreasing(c) Apply the First Derivative Test to identify the relativeextremum. (If an answer does not exist, enter DNE.)relative maximum (x, y) =relative minimum (x, y) =
Ross has a laser sight for golf that gives him the straight line distance to any object he points the sight at. From an elevated tee block, he uses the sight and finds that the straight line distance to the green is 278 meters. He also determines that the angle of depression to the green is 52°. What is the height of the elevated tee block above the level of the green?
Options:a) 219mb) 305mc) 191md) 171m
Find the relative extrema of the following function of twovariables. f(x, y) = e^x^2 + y^2Find all critical point(s). Write your answer as a point, (x,y).Critical Point: (a, b) =(0,0) CorrectTest the critical point to determine what it is. You testcritical points as follows. Find the determinant function:D(x, y)=
The length of a rectangle is increasing at a rateof 4 cm/s and its width is increasing at a rateof 9 cm/s. When the length is 7 cm and thewidth is 4 cm, how fast is the area of the rectangleincreasing? Answer is in cm^2/s
Given a curve:r(t) = (t^2 - 2t, ((1/2)t - 1))Find its velocity and acceleration when the speed is minimum. What's the angle between the velocity vector and acceleration vector at that moment?
