I thought such a title would draw people in to my topic.

Okay. I got a large calculus test coming up on Tuesday. I am currently reviewing like mad. I’ve worked out some of these questions, and my instructor said they were done incorrectly. There’s about 100 review questions, but I’ll pick out like 10, one from each time, and put it on these here forums. If you all can get the answer, with proving it with steps, and post it here; it’d help me critically in my understanding of calculus.

<strike><b>1. In a geometric sequence of real numbers, the sum of the first six terms is nine times the sum of the first three terms. If the first term is 5, what is the third term?</b></strike>

<strike><b>2. Let f(x) = {x^3 - 6x^2 + 9x, for 0<&=x, and x<&=4},{-x + 7, for 4<x, and x<&=7}

a) For 0<&=x, and x<&=7, determine the intervals in which the function <i>f</i> is decreasing.

b) Ommitted.

c) Does Lim x->∞ exist? Explain.</strike>

<strike>3. The sum of the infinite series, c/2 + (c/2)^2 + (c/2)^3 + … is 2. Determine the value of <i>c</i>.</strike>

<strike>4. Consider the arithmetic sequence where t1 + t3 + t5 + t7 + t9 = 17, and t2 + t4 + t6 + t8 + t10 = 15. Find <i>d</i>.</b></strike>

<b>5. Find the arithmetic sequence with first term = 1, and constant difference is not 0, whose second, tenth, and thirty-fourth terms are the first three terms on a geometric sequence.</b>

Yeah, just reading that confuses me.

<strike><b>6. At what numbers is F(x) = (3|x|-x^2)/([x^0.5]+x^(1/3))</b></strike>

There’s like a billion others, but I got those. But if you can explain with numbers and/or words how you answer them or even show the answers, it’d be REALLY appreciated.

ANSWERED: 1, 2, 3, 4, 6