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Calculus
The branch of mathematics that deals with the study of continuously changing quantities, with the use of limits and the differentiation and integration of functions of one or more variables, is called Calculus. Calculus analyzes aspects of change in processes or systems that can be modeled by functions. The English physicist, Isaac Newton, and the German mathematician, G. W. Leibniz, working independently, developed calculus during the 17th century.
25,068 Questions
What is the answer to y equals x plus 2x plus 5?
y = x + 2x + 5 can be simplified by combining the x values. This results in y = 3x + 5. This equation can't be simplified any further or solved for either variable.
Actually the equation can be solved even further by finding the (X,Y) values. y = 3x + 5 is in Slope intercept form (y = mx + b). One can find the value of each by substituting the opposite variable with 0.
Let's solve for X.
0 = 3x + 5
-3x = 5
x = -1 2/3.
Now let's solve for Y.
y = 3(0) + 5
y = 0 + 5
y = 5
So (-1 2/3, 5) are the coordinates for your slope.
What is 2x squared plus 24 equal zero?
so x squared + 12 = 0 so xsquared = -12 which lands you in the realm of imaginary numbers. The square root of -12 is 2i root 3 where i is the imaginary sqrt of -1.
What is the difference between inscribed and circumscribed in integration?
When rectangles are inscribed, they lie entirely inside the area you're calculating. They never cross over the curve that bounds the area. Circumscribed rectangles cross over the curve and lie partially outside of the area. Circumscribed rectangles always yield a larger area than inscribed rectangles.
What is Phi to the first A digits?
If you mean the golden ratio, that's approximately 1.618033988749894848204586834... The exact value is (1 + (square root of 5)) / 2.
How you will know that the graph and the given equation into variables represent a function?
The graph or function relates a value y (in the vertcal direction) to a value x (in the horizontal direction).
For each point x in the domain, there must be one and only one value y. In terms of a graph that means that a vertical line from any value of x in the domain must meet the graph in exactly place - at least once and not more than once. More than one x values can have the same y value associated with them.
How to identify the graph of a function?
Every function is a graph. So the only thing is to distinguish functions from other graphs.
One formal convention actually define function as its graph, and a graph is the set of all ordered pairs (x, y)
A function is a special graph where it's set set of all ordered pairs (x, y) where y = f(x). f(x) is unique (or rather one goes in only one comes out), meaning for each x, there is one and only one y. (Note: For each y, there might be many x)
So to test this, we use a "vertical line test". The idea is for all x in the domain of f, say A, we draw a vertical line (x = a for some a in A), it only intersect the graph of f one and only once. Of course, there are infinity many points, you have to do it infinitly many times. Therefore, you can do it generacally:
Let A:= dom f
For all a in A, f is a function if and only if (x = a implies f(x) = f(a) and nothing else)
Find the multiplicity root of the equation x3-x2-x plus 1 equals 0 near x0 equals 0.9?
The end part of the question does not seem to make sense.
The equation has three real roots, a single root at x = -1 and a double root at x = 1
Is x equals -3 a solution to the equation 2x plus 8 equals 3x plus 11?
According to my calculations, yes.
2x+8=3x+11 -8
2x=3x+3 -2x
0=x+3 -3
-3=x
What is an example of an equation that makes the graph of y equals x less steep?
A slope greater than 1 makes a graph be really steep. On the other hand, a slope less than 1 but greater than 0 makes a graph less steep. Therefore any fraction slope would give you a less steep graph.
An example could be y=(1/3)x.
What kind of line has a slope of 0?
A horizontal line, such as Y = 3, has a slope of zero.
Slope is the limit, as delta x approaches zero, of delta y / delta x.
What does 0.04 kL equals in mL?
to figure this out just remember the acronym:
K ing
H enry
D ied
M onday
D rinking
C hocolate
M ilk
Kilo Hecta Deca Meters(Unit) Deci Centi Milli
0 . _ 0_ _ _4_ _ _ _ _ 0 _ _ _ 0 _ _0 _ _0 .
Start the decimal point on the starting unit. Move the decimal point over until you get to the one you want, in this case mL.
So, you get 40,000 mL.
(sorry about the underscores, It wouldn't let me put spaces.)
How are equations and inequalities similar?
The boundary of an inequality is formed by the corresponding equation.
How do you solve y to the 3 plus 9y plus 10y-5 divided by y plus 2?
y3 + 9y + 10y - 5/y + 2 can not be solved, as it is not an equation. If you would like to simplify it, you can reduce it a bit:
= y3+ 19y - 5/y + 2
How do you solve 2s-19 equals 29 in equations?
First, add 19 on both sides. You end up with 2s = 48. Then divide both sides by 2 in order to isolate the 's'. You get s = 24.
What is the solution to -2 - 3x equals 10?
-2 -3x = 10
Add 2 to both sides: - 3x = 12
Divide both sides by -3: x = -4
