“How’s your Mary doing?”.

“She’s doing well. She’s 8 now. She’s in Grade 3. She really enjoys the Pre-Algebra and the Pre-Textual Analysis.”.

“How’s your Mary doing?”.

“She’s doing well. She’s 8 now. She’s in Grade 3. She really enjoys the Pre-Algebra and the Pre-Textual Analysis.”.

Filed under algebra, education, language in math, teaching

As h approaches zero

I quietly despair.

It really is the limit.

Please don’t take me there.

The funny thing about the calculus is that it was brought into existence by Isaac Newton in 1666 or earlier, and was developed and used without the idea of limits for over 150 years. The first attempt to get rid of the troublesome infinitesimals was by Cauchy in 1821, where he introduced the chord slope (f(x + h) – f(x))/h. The whole business of finding a satisfactory definition of the derivative was finally achieved by Weierstrass in the mid 19th century.

So here we go with cubics, and the same approach can be used for any whole number power of x, even negative ones. You should try it.

Next time sin(x) and cos(x), so no more sin(h)/h stuff.

Since the kids have to explain everything in the new CCSS math standards,

they better have this under their belt, even if they have to learn it and parrot

it out in some test or other (careful, cynicism is not always just round the

corner).

So, here is a long division calculation for you, 32 divided into 2768, or if you

prefer the old fashioned, only used in schools notation, 2768 <the old

fashioned division sign, not on my keyboard> 32. (and < and > are not

representing inequalities at this point).

Division is at bottom repeated subtraction, so we do it:-

32)2768 100×32 = 3200 is too big

2560 so take a smaller multiple (in 10’s)

—— Choose from 90×32=2870, 80×32=2560 (OK!)

208 and subtract,leaving 208, and 10×32=320

192 So try 6×32=192 (OK!). 7×32 is too much.

—- Subtract again, leaving 16,which is less

16 than 32 and so is the remainder.

So 2768 = 90×32 + 6×32 + remainder,

which is 96×32 + 16,

and so 2768 divided by 32 is 96 with remainder 16

The End

Filed under arithmetic