Help on Cal problems

Pre-College Topics High School Life
1

<p>My teacher gave me a package over the Spring Break. After nine days of fun and games, I started to work on the problems. I know how to do most of the problems, with some I struggled on. Here are the multiple choice questions. I desperately need your help. Thanks in advance. :)</p>

<p>1) A rectange with one side on the x-axis has its upper vertices on the graph of Y=cos x. What is the minimum area of the shaded region. This is the figure that's shown on the paper.<a href="http://img162.imageshack.us/img162/2588/calbc9ni.jpg%5B/url%5D"&gt;http://img162.imageshack.us/img162/2588/calbc9ni.jpg&lt;/a&gt;&lt;/p>

<p>A) 0.799 B) 0.878 C) 1.140 D) 1.439 E) 2.000</p>

<p>I can only eliminate the choice E, because 2 is the total area of the parabola. </p>

<p>2) If the function F is defined by F(x)= Square root of (X cube + 2) and G is an antiderivative of F such that G(3) = 5, then G(1) =</p>

<p>A) -3.268 B) -1.585 C) 1.732 D) 6.585 E) 11.585</p>

<p>I know I need to integrate the F(x), but I just don't know how. I mean I can't use Substitution. </p>

<p>3) A particle moves along the X-axis so that at any time t>0 its velocity is given by v(t) = ln(t+1) - 2t+1. The total distance traveled by the particle from t= 0 and t=2 is</p>

<p>A) 0.667 B) 0.704 C) 1.540 D) 2.667 E) 2.901</p>

<p>I know I have to set the velocity function to zero in order to find the interval. But I don't know what t value is to get ln(t+1) - 2t = -1. </p>

<p>Thank you in advance. :)</p>

2

<p>3) If you can use your calculator, instead of setting v(0) equal to 0, you can just hit MATH 9 and then enter abs(ln(x+1)-2x+1),x,0,2 and hit ENTER.</p>

<p>2) integral from 1 to 3 of f(x) = g(3) - g(1). Plug in 5 for g(3), use your calculator for the integral, then solve for g(1).</p>

<p>1) Let A(x) represent the area of the not-shaded region. When A(x) is a minimum A'(x) = 0. First you determine that A(x) = 2x*y = (2x)(cosx), so A'(x) = 2cosx - 2xsinx. Set that equal to 0, solve for x on your calculator, and plug that into A(x) to determine the area of the not-shaded region. Then subtract that from 2 (or whatever the area of the shaded + not-shaded region is) and that's your answer.</p>

<p>I don't have my calculator at home today cause I lent it to my friend. :)</p>