CPhill

If this is (2x+3)/(5x+7)...the limit of this as x approaches infinity is just (2/5)....remember..... we have a "same over the same" condition, here.....which means that, in a rational function, when the polynomials in the numerator and the denominator are of the same degree.....the function has a limit as x → ∞  = the ratio of the coefficients on the highest power of each polynomial.....

Here's a graph......

Heureka....I'm trying to learn more about how to manipulate these series questions....I followed everything except for this.....

How did you get from [b₁(a₁ - d)]*r^n-1    to     [b₁(a₁ - d)] / (1 - r)    ???

Thanks in advance.....

It's just  (1/15) * 65 ......

You should be able to take it from there....

Well  10% of 762 = 76.2

So....20% must just be twice as much.......

Can you take it from there...??

Let's see, Sasini....

u + 1/2 = 31/4     subtract 1/2 from both sides

u = 31/4 - 1/2      get a common denominator

u = 31/4 - 2/4

u = 29/4  = 7 + 1/4 = 7.25

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Ah...I see ...we just interpreted this one differently..!!!!!....

Your answer is good, too....!!!

Here's the graph....notice that it does not intercept the x axis.....thus, no real roots

Mmmm   ....let's look at this one again, saseflower..

(1/3 )  / 9  =

(1/3) / (9/1)  =

1/3   x  1/9  = 1/27

Remember, the reciprocal of 9 = 1/9  ...

(I gave you points for a good try, anyway)

-2x^2+7x=10   subtract 10 from both sides

-2x^2 + 7x - 10  = 0

Note that  b^2 - 4ac = 49 - (4)(-2)(-10) = 49 - 80 = -31

So......this polynomial has no real roots...!!!

30,28,12,and 14

(30 - 28)^2 - (14 - 12) =

(2^2)  - (2) =

4  - 2  =

2