CPhill

rosala and zegroes should have more respect for their elders...!!!!    (LOL!!).....particularly......"old fossils"

Long ago???...heck...at my age, yesterday is a blur....!!!!

About 8 minutes....

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Cerca de 8 minutos....

Nice one, rosala.....I knew it would be easy for you....!!!!

Thumbs-Up and 3 points from me......

Perimeter is given by....

P = 2(W + L)    so we have.....

18 = 2 (W + L )  divide by 2

9 = W + L     subtract W from both sides

9 - W  = L

Now...the area "formula" is given by

A = W * L    and we have

20 = W * L      ans substituting (9 - W) for L, we have

20 = W * (9 - W)

20 = -W² + 9W   .....Rearranging this gives

W² - 9W + 20 = 0

Factoring , we have

(W - 5) (W - 4)  = 0

And settong each factor to 0, we have either W = 4 or W = 5.....(depending on how we "orient" the rectangle.....)

We have.....

  lim          [ 6/(x+h) - 6/(x) ]   / h    =      

(h→0)

6*lim          [ 1/(x+h) - 1/(x) ]   / h    =    

   (h→0)

6* lim  [ (x) - (x+h)] / [(h)*(x)*(x + h)]  =

    (h→0)

6 * lim [-h] / [(h)*(x)*(x + h)]   =

     (h→0)

-6 * lim [ 1 / ( x² + xh) ]  =

      (h→0)

Now, let (h→0) and we have......

-6/x²   or    -6x^-2

Very nice, Alan....!!!

The employment of the Taylor series is a new one for me....(definitely a "tool chest" item!!)....When I was in school, I always wondered what the Taylor and McLaurin series were actually used for (other than to express something in terms of a polynomial!!)....I'm going to recommend this one as part of Melody's "End of the Day" Highlighted Problems...

Thumbs-Up from me....!!!

Let's take these inequalities one at a time..

x + 1 < 4     subtract 1 from both sides

x < 3

And the second inequality is

x - 8 > -7  add both 8 to both sides

x > 1

The  "∩" means "intersection"....we are asking...."What interval makes both inequalities true??"

Notice that the interval that makes both true is  1 < x < 3  which we can also denote as...(1, 3)

8^-8= ? *8^2    ....divide both sides by 8^2

(8^-8) /(8^2)  =  

(8^-8) * (8^-2)  =

8^-10

And that's the missing factor....

Here's the graph......