CPhill

At the bottom left of the calculator next to the "pi(e) a la mode"  button.....

I'll trade you one "Integration By Parts" lesson for one "Parametric Equations as they apply to Parabolas" lesson.....

Deal???

Here's the prime factorization from Wolfram Alpha.......

(I'll take their word for it.....!!!!)

If you read Isaac Asimov's essay, "The Imaginary That Isn't," he demonstrates that an "imaginary" number isn't any more "imaginary" than any other number!!!  (He does so with great humor, too!!).....all of Asimov's essays on mathematics are excellent...and easy to understand....I highly recommend any of them !!!!

(Asimov even demonstrates that there is no such thing as a "half a piece of chalk!!"

Aw shucks, folks.....it was nothing....really......!!!

Geno had logic out the ying-yang....me???....I was just throwing something against the wall and hoping that some part of it would stick !!!!

f(x) = x^4 - 4x^2 - 3

f'(x) = 4x^3 - 8x

Setting the first derivative to 0 to find the critical points, we have

4x^3 - 8x = 0    factor

4x(x^2 - 2) = 0      and setting each factor to 0 we have    x = 0,  x =±√(2)

And finding the second derivative, f"(x),  we have ....  12x^2 - 8

And "plugging the critical points into this we have

f"(0) = -8    so the curve is concave down at x = 0

And

f"(±√(2)) = 12(2) - 8   = 24-8 = 16, so the curve is concave up at x=  ±√(2)

So, the curve is concave down on  (-√2, √(2 ) = (-1.414, 1.414)

what is a thirteen over five times b two over 2 divided by a negative seven over ten times b negative one over three?

(13/5)  x (2b/2) / (-7/10) x (-b/3) =

(13/5)  x b / (-7/10) x (-b/3) =

(13b/5) x (-10/7) x (-b/3)  =

(-130b/35) x (-b/3) =

(130b^2  /  105)  =

(26/21)b^2

If b = 4   then  (b -2^2) = (4 -2^2) = (4-4)  =  0

But, we'd be dividing 100 by 0 and that's undefined....thus.....there is no "answer" here!!!

There is no sloution to this.

If we add three consecutive odd integers we get an odd result..........and subtracting 21 from this is an even result.

And that can't be equal to "the smallest odd'.....or any other odd !!!!!