PreCalculus Study Guide

[BlasianAsian]

I took one look at the pre-cal sample CBE. For the first semester.

Hmmm....Might be a LITTLE tougher than I thought. So, tengo muchas preguntas para sois. =D

1) Okay. So they talk about converging and diverging geometric sequences. I looked # and managed to determine that convergent equations go toward 1, and divergent go...uhh...everywhere? IDK. Anyway, here's the problem:

Fine the limit [unparseable or potentially dangerous latex formula], the number of terms, approaches infinity for the sequence and series of [unparseable or potentially dangerous latex formula]. If they converge, give the value and if they diverge, state so.

Series [unparseable or potentially dangerous latex formula] = [unparseable or potentially dangerous latex formula]

Answer: I know how to find the sum: 13.5

This is foreign to me:

Sequence [unparseable or potentially dangerous latex formula]

Could somehow tell me how and when to construct this type of equation?

2) Here's another one!

Give the equation of the tangent line to the graph of the function [unparseable or potentially dangerous latex formula] at the value [unparseable or potentially dangerous latex formula].

Answer: [unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]

I know how to do the f prime thingy. I just don't know when to use it...can you list some situations you would need to use the prime thingy in pre-cal? Thx!

Halp! >.<

[rcoker7]

ok I might be bad at explaining this but I'll go for it anyway.

1) The foreign looking equation is read "The limit as x approaches infinity of 9/3^n-1=0". This means that as x gets unbelievable large(or approaches infinity), the equation approaches zero, because 9/(some huge number) approaches zero. The word "approaches" is extremely important because x will never actually reach the stated value(in this case infinity) but will get extremely close to it. The question will usually tell you if you need to use it or not.

2) f'(x)(also called the derivative) is used to find the slope of the tangent line at any point on an equation. Since you already know how to find them I won't go into too many details(you'll get those in calculus). You just need to use it whenever you need to fine slopes on complicated curves(i.e. not linear)

[BlasianAsian]

Ok! Got the second one, but for the first one, I need to know how to create the foreign looking equations. =D

[rcoker7]

What do you mean by create them? Like the notation?

[FabensMath]

[BlasianAsian]

Like, how do you create the equations?

[rcoker7]

Ok I think I understand what you're asking. You just write lim x->n (the function)=????? (x->n is a subscript) where n is the value x is approaching and the right hand side is the value y is approaching at that point.

[BlasianAsian]

Ok. I STILL don't quite get it. A little more explanation please?

[007math]

This is first semester Pre-Cal? I'm pretty sure we learned limits and series in second semester.....(at least in our school).

Convergent doesn't mean it converges to 1, it means it has a finite value. Basically, the series will not go off to infinity or negative infinitiy but instead "converge" to a value (so that 9, 3, 1, 1/3 series converges).

[BlasianAsian]

Oh. So the B series converges to 0?

Still need help constructing the equation. This is so much harder than I thought it was gonna be. I still wanna be in cal next year. Just imagine. A whole hoard of seniors. Then, *puts on shades*, A SOPHMORE WALKS IN. Slow motion, everyone's heads turn.

["Who let the Dogs Out?!" plays in background]

XD

[nsguy1350]

[007math]

I'm not sure what equation you mean, but do you mean this:

[unparseable or potentially dangerous latex formula]

or

[unparseable or potentially dangerous latex formula]

The first is for a series and the second is for a sequence. A series are the terms summed up, a sequence is just the terms. As you can see, I used the summation notation for the series basically what the second one says is that what happens do your term as x goes on and on? If x were a huge number, (1/3)^x would get smaller and smaller (almost hitting 0) so we can say that the limit would be 0.

[BlasianAsian]

But, to achive this goal, I STILL need help constructing the limit equation, as stated in original post. Halp plz!? >.<

[was]

9, 3, 1, 1/3, 1/9, ... = 9/1, 9/3, 9/9, 9/27, 9/81, ... = 9/3^0, 9/3^1, 9/3^2, 9/3^3, 9/3^4, ... = 9/3^(n-1)

[nsguy1350]

For sums and limits guys, try putting "\displaystyle" at the very beginning of your LaTeX.

[BlasianAsian]

Ok........................how did you do that?

'Cmon man, I don't have ESP!

[was]

A geometric sequence is of the form a, ar, ar^2, ar^3, ... where r is the ratio of the terms. So it will be ar^(n-1) where n is the number of the term. For 9, 3, 1, 1/3, 1/9, ... , a = 9 and r = 3/9 = 1/3. 9(1/3)^(n-1) = 9(1^(n-1))/(3^(n-1)) = 9/3^(n-1)

[BlasianAsian]

You sir, are a genius. Or I'm just an idiot. Either way, that's one question down! 74 more to go...

[was]

A geometric sequence will converge to 0 if |r|<1 and diverge if |r|>1.

[BlasianAsian]

Checked and stored!