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Questions in Grade College

[Jawaban] Assignment 1: Sequences and Series 1. Determine whether each of the following sequences converges. If it does, find the limit: (a) $a_n=\frac{n}{n+1}$ (b) $b_n=\frac{(-1)^n}{n}$ 2. Test the convergence or divergence of the series: (a) $\sum_{n=1}^{\infty} \frac{1}{n^2}$ (b) $\sum_{n=1}^{\infty} \frac{n}{n+1}$ 3. Use the Ratio Test to determine the convergence of: $\sum_{n=1}^{\infty} \frac{3^n}{n!}$ 4. Determine whether the series $\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}$ converges absolutely or conditionally. 5. A geometric series has first term 5 and ratio $r=\frac{2}{3}$. Find the sum of the series.

[Jawaban] An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

[Jawaban] What is the y-intercept of $f(x)=\left(\frac{1}{4}\right)^x$? A. $(0,1)$ B. $\left(1, \frac{1}{4}\right)$ C. $(0,0)$ D. $(1,0)$

[Jawaban] Which of the following quotes from The Great Gatsby is an example of direct characterization? A. "I'll tell you a family secret," she whispered enthusiastically. 'It's about the butler's nose. Do you want to hear about the butler's nose?' 'That's why I came over tonight." B. "All my aunts and uncles talked it over as if they were choosing a prep school for me, and finally said, 'Why --ye-es,' with very grave hesitant faces" (Fitzgerald 3). C. "I am inclined to reserve all judgments, a habit that has opened up many curious natures to me..." (Fitzgerald 1).

[Jawaban] Write a polynomial [tex]f(x)[/tex] that satisfies the given conditions. Polynomial of lowest degree with zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with [tex]f(0)=320[/tex].

[Jawaban] Based on the chart, which nation can expect to experience the most social issues of a developing country? | | | | :------- | :-------- | | Angola | $2.784 \%$ | | Iraq | $2.345 \%$ | | United Kingdom | $0.553 \%$ | | United States | $0.9 \%$ | A. Angola B. Iraq C. United Kingdom D. United States

[Jawaban] If [tex]f(x)=3 x+\frac{5}{x}[/tex], what is [tex]f(a+2)[/tex]? A. [tex]3(a+2)+\frac{5}{a+2}[/tex] B. [tex]3 a+\frac{5}{a}+2[/tex] C. [tex]3(f(a))+\frac{5}{f(a)+2}[/tex]

[Jawaban] Which of the following are equivalent to the function [tex]$y=3 \cos x+2$[/tex]? Check all that apply. A. [tex]$y=-3 \cos x-2$[/tex] B. [tex]$y=3 \sin \left(x+\frac{\pi}{2}\right)+2$[/tex] C. [tex]$y=3 \cos (-x)+2$[/tex] D. [tex]$y=3 \sin \left(x-\frac{\pi}{2}\right)+2$[/tex]

[Jawaban] Which of the following does NOT have an effect on wire resistance? A. temperature B. type of power C. wire length D. material

[Jawaban] Subtract. $\frac{y}{10 a k^2}-\frac{5 a u^3}{4 b^2 k}$ Simplify your answer as much as possible.