Calculus

Yes.

y = 5

Divide the volume in cm3 by 1 000 000 so the answer is 0.225 cubic metres.

6x * 9x = 6 * 9 * x * x = (6*9)*(x*x) = 54*x2

x= 23

Destructive Interference

8

The answer is 35. 2x2-6x+15

2(-2)2-6(-2)+15

8+12+15

35.

And this is not calculus...

y = 2x^2 + x -1

If you know calculus you can find the minimum or maximum when the slope of the equation is zero. This is the first derivative of y with respect to x

dy/dx = 4x +1 = 0

4x = -1

x = -1/4

y = 2 (-1/4)^2 -1/4 -1 = 1/8-1/4-1 = 1/8 - 2/8 - 8/8 = -9/8 minimum = -1.125

Suppose x3-4x = 0. To solve, factor:

x3-4x = x(x2-4) = x(x+2)(x-2) = 0 Now, a product equals 0 if and only one or more of the factors equals 0, so set each factor to 0 and solve.

The roots are 0,-2 and +2.

Y = 2bx

divide both sides by 2b

Y/2b = x

You can use the rule for multiplying derivatives.

LOL, all proof is done the same ---- direct, contradiction or induction.

An epsilon-delta proof is what a very conventional definition of limits of functions.

The proper definition of a limit of a function is, given a real(or complex) function f, we say lim f(x) = b as x approaches a if:

For all ε > 0, there exist δ > 0 such that for all x in the domain of f, if x != a and |x - a| < δ implies |f(x) - b|< ε

The intuition is quite easy, though the difficult look. It simply says no matter how small of an interval centered at x = a, we can always squish an interval around f(x) = b into it. Doesn't that mean if x goes to a, where the interval is so small, the point it goes to is b?

Just do everything you can to reduce it to the definition or equivalent.

In Non-standard analysis, there is a slightly different way of doing it.

Extend the line until it hits the x axis and that is the x intercept. If the line is not parallel to the x axis, then extending it one way will reach the x axis, the other way will not. If the line is parallel to the x axis it will never meet it (or, if you like, it will meet it at plus or minus infinity, which is another way of saying never).

Just like any other job, how soon you finish depends on how fast you work.

If you count 1 every second, never make a mistake and never take a break,

you finish this particular job in 11days 13hours 46minutes 40seconds.

It is an equation and the value of x is 8

x = 90

y = 89

It is the infinite set of points of the form [x, (4x+9)/7] for all value of x in its domain.

yes

y = 15 - 8x/3

y - 15 = -8x/3

15 - y = 8x/3

x = 3/5(15 - y)

and so x = 9 - 3y/5

e3x+5 x ex =7

e3x+5+x=7

4x+5=ln(7)

x=(ln(7)-5)/4

800

6x+3=27

6x=24 (subtract 3 from each side) x=4 (divide both sides by 6)