Calculus

(-5, 2)

Because we muliply the three sides of a cube of one meter length x 3. =1000x1000x1000=1,000,000

12.6

x = 104

The differentiation of sin x plus cosx is cos (x)-sin(x).

You don't use a "formula" to multiply numbers. You just go ahead and multiply them.

14

The maximum movement from the middle position.

It is a one word name ; 'Calculus'.

There are two (main) ways to graph this parabola.

The first is to simply substitute in values of x, find the corresponding y values and then plot those points and connect the points with a curve.

The second way is to 'complete the square' so that we can find where the maximum or minimum occurs and the y-intercept and graph from those two points. This is the process described below.

y = -x2 + 8x + 5

y = -(x2 - 8x) + 5

y = -(x2 - 8x + 16 - 16) + 5

y = -(x2 - 8x + 16) + 16 + 5

y = -(x-4)2 + 21

From this we can see that a maximum occurs at (4,21). To find the y-intercept, substitute in x=0, giving y=5.

From these two points, we get a pretty good idea of what the graph looks like. If you want more accuracy, substitute in more values of x.

(1, 0)

Intuitively, a continuous function y = f(x) is one where small changes in x result in small changes in y.

More rigorously, consider the function y = f(x) defined on the domain D to the codomain C where both D and C are subsets of R.

Then f(x) is continuous at a point p in D if the limit of f(x) as x approaches p within D is f(p).

The function is said to be continuous is it is continuous at every point in its domain.

The domain and codomain of f can be extended to multiple dimensions provided a suitable metric (eg Pythagorean distance) is used.

IF you use 39.37 inches to a meter (pretty close), there are 60 inches in 5 feet. 60/39.37 = 1.524003048 meters

89067777782345637

3x = 70

x = 70/3 or 23 and 1/3

X2 - 5X - 6 = 0

What two factor of - 6 add up to - 5 ??

(X + 1)(X - 6)

So,

X = - 1

===

x represents an unknown number.

6 + 7x = -36

first, subtract 6 from both sides

7x = -42

then, divide both sides by 7

7x/7 = -42/7

x = -6

to check, put -6 back into the original equation:

6 + (7 x -6) = -36

6 - 42 = -36

Reading this as:

4x2-6=2x2

This implies that:

-6=-2x2

3=x2

x=sqrt(3) and x=-sqrt(3)

So x can equal plus or minus the square root of 3

First, you look at the equation long enough to recognize that it's the equation

of a straight line with [ slope = 1 ] and [ y-intercept = 0 ].

Then you draw that line. It passes through the origin, and slopes up toward the

right at 45 degrees.

As another technique, you could use the equation to calculate two points on the line,

then mark the points on the graph, and draw a line between them.

To calculate two points, choose two values for 'x', and then calculate the value

of 'y' for each one.

Let's just pick two numbers out of the blue for 'x':

x = 2 and x = 9 .

Can you use the equation [ y = x ] to calculate the value of 'y' that goes with each one ?

That's right. Good work. When x=2, 'y' is also 2. And when x=9, 'y' is also 9.

So now you have two points on the graph ... (2, 2) and (9, 9).

Using a soft pencil, mark each of those two points on your graph with a small dot.

Then, using the same pencil along with a ruler, draw a line that connects the two

dots. You can extend the line as far as you want to, past either point, in either direction.

(5y + 3)(y - 1)

your equation is this...

2x < y + 7

Now solve for y...

2x - 7 < y

Since you have two variable the most you can get out of (y) is the graph and the y-intercept.

the y-intercept is y > -7

5x - 10 = 3x + 2

5x - 3x = 2 + 10

2x = 12

x = 12/2

x = 6