I tutored middle schoolers in science and mathematics subjects throughout the course of my academic year.
Determining Convergence or Divergence In Exercises $27-34,$ test for convergence or divergence, using each test at least once. Identify which test was used.
$\begin{array}{ll}{\text { (a) } n \text { th-Term Test }} & {\text { (b) Geometric Series Test }} \\ {\text { (c) } p \text { -Series Test }} & {\text { (d) Telescoping Series Test }}\end{array}$(e) Integral Test (f) Direct Comparison Test(g) Limit Comparison Test
$\sum_{n=1}^{\infty} \frac{\sqrt[3]{n}}{n}$
(a) Express the area under the curve $y=x^{5}$ from 0 to 2 as a limit.(b) Use a computer algebra system to find the sum in your expression from part (a).(c) Evaluate the limit in part (a).
Find the lengths of the curves in Exercises $1-12 .$ If you have a grapher,you may want to graph these curves to see what they look like.$$y=(3 / 4) x^{4 / 3}-(3 / 8) x^{2 / 3}+5, \quad 1 \leq x \leq 8$$
Find the lengths of the curves in Exercises $1-12 .$ If you have a grapher,you may want to graph these curves to see what they look like.$$y=\frac{x^{3}}{3}+\frac{1}{4 x}, \quad 1 \leq x \leq 3$$
A) Let f(x) = x^2 + bx + c. Assume that f has an absolute minimum at x = 6 and the graph of f passes through P = (0, 2). Then c - 7b = ?B) Let f(x) = (x^3)/6 - x^2 + 3x + 2 and I = (c, f(c)) be the inflection point of y = f(x). Then 2c + f'(c) = ?C) Let f(x) = x^2 + px + 1. Assume that f(x) satisfies the hypothesis of Rolle's theorem on the interval [5, 10] and c ∈ (5, 10) satisfying the conclusion of Rolle's theorem. Then 2c - p = ?
Brianna is taking out a personal loan. She is given a 4.5%variable interest rate. What does this mean?Select one:a.Brianna can expect her interest rate to start at 4.5%, butchange throughout the term of her loanb.Brianna can expect her APR to be 4.5% throughout the term of herloanc.Brianna can expect her interest rate to be 4.5% throughout theterm of her loand.Brianna can expect to pay back her principal plus 4.5%interest
Edgar accumulated $6,000 in credit card debt. If the interestrate is 20% per year, and he does not make any payments for 3years, how much will he owe (in dollars) on this debt in 3 years byeach method of compounding? (Simplify your answers completely.Round your answers to the nearest cent.)(a) compound quarterly $_____(b) compound monthly $________(c) compound continuously
A fair coin is continuously flipped. What is the probabilitythat the pattern T,H,H,H occurs before the pattern ofH,H,H,H?(a) Derive the result theoretically.(b) Write a simulation code to find the answer using relativefrequency by preforming the simulation N=10000 times. Compare yoursimulation result with the theoretical answer from part (a).
Model the data using an exponential function f(x) = Abx. x 0 1 2f(x) 128 64 32 f(x) =
Find the components for the vector projection of (12,5) onto(-9,12)
