# Review questions (conics, etc.)

• May 22nd 2007, 06:45 PM
Mulya66
Review questions (conics, etc.)
Hello all,

Just reviewing for the finals and stumbled upon some questions I'm having issues with. Conics mostly (I literally failed that chapter way back when).

1) "Find the focus of the graph y = 1/8(x-2)+3

2) "Find the sum of the series: -1 + 2 + 5 + 8... +56" (for this one, I resulted with S(19.3333) = 531.6657. Which is not one of the multiple choice answers).

3) "f(x) = x-4 and g(x) = x^2, find g(f(3))"

4) "Find the foci of the ellipse x^2+9y^2=81"

5) "Find the verticle asymptotes f(x) = x-1/x^2-25"

• May 22nd 2007, 07:05 PM
topsquark
Quote:

Originally Posted by Mulya66
2) "Find the sum of the series: -1 + 2 + 5 + 8... +56" (for this one, I resulted with S(19.3333) = 531.6657. Which is not one of the multiple choice answers).

This is an arithmatic series
$\displaystyle a_n = a_0 + nd$
with
$\displaystyle a_0 = -1$
$\displaystyle d = 3$

The sum of this series is:
$\displaystyle S = \sum_{n = 0}^N (-1 + 3n) = \sum_{n = 0}^N (-1) + 3 \sum_{n = 0}^N n$

$\displaystyle = -(N + 1) + 3 \cdot \frac{N(N + 1)}{2}$

So what's N?
$\displaystyle a_N = 56 = -1 + 3N \implies N = 19$

Thus
$\displaystyle S = -20 + 3 \cdot \frac{19(20)}{2} = 550$

-Dan
• May 22nd 2007, 07:06 PM
topsquark
Quote:

Originally Posted by Mulya66
3) "f(x) = x-4 and g(x) = x^2, find g(f(3))"

$\displaystyle f(3) = 3 - 4 = -1$
$\displaystyle g(f(3)) = g(-1) = (-1)^2 = 1$

-Dan
• May 22nd 2007, 07:08 PM
topsquark
Quote:

Originally Posted by Mulya66
5) "Find the verticle asymptotes f(x) = x-1/x^2-25"

I presume this is:
$\displaystyle f(x) = \frac{x - 1}{x^2 - 25}$

Then
$\displaystyle f(x) = \frac{x - 1}{(x + 5)(x - 5)}$

Thus the function goes to infinity (ie. is undefined) at two x values, x = -5 and x = 5. These are your vertical asymptotes.

-Dan
• May 22nd 2007, 07:11 PM
Mulya66
Quote:

Originally Posted by topsquark
$\displaystyle f(3) = 3 - 4 = -1$
$\displaystyle g(f(3)) = g(-1) = (-1)^2 = 1$

-Dan

I just got that, too. But I'm perplexed on the answer choices provided by the book. The choices are 144, -1, 1, and 5. Obviously, it's either B) -1 or C) 1. What should I do in a case like this? My instincts are going with C) 1...

Thanks.
• May 22nd 2007, 07:17 PM
topsquark
Quote:

Originally Posted by Mulya66
I just got that, too. But I'm perplexed on the answer choices provided by the book. The choices are 144, -1, 1, and 5. Obviously, it's either B) -1 or C) 1. What should I do in a case like this? My instincts are going with C) 1...

Thanks.

-Dan
• May 22nd 2007, 07:21 PM
Mulya66
Quote:

Originally Posted by topsquark