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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 differentence between calculus and vector calculus?

Hence the reason for why it is called Vector Calculus, Vector Calc. is simply an expansion in the calculus subject are in math. It deals with Taylor's Formula (in calc 2 you learn the taylor polynomial and the taylor series), theorems from Green, Gauss, and Stokes, and much more.

How do you solve x-7y equals 18 2x-7y equals 22?

x - 7y = 18 ... (A)

2x - 7y = 22 ... (B)

Equation (B) - equation (A) gives

x = 4

Substituting this value of x in equation (A) gives

4 - 7y = 18

or 7y = -14 which gives y = -2

Solution: (x, y) = (4, -2)

How do you figure out y equals 2x 6x-y equals 8 by the elimination method?

y = 2x

6x-y = 8

Rearrange the top equation:

-2x+y = 0

6x-y = 8

Add both equations together in order to eliminate y:

4x = 8

Divide both sides by 4 in order to find the value of x:

x = 2

Substitute the value of x into the original equations in order to find the value of y:

Therefore: x = 2 and y = 4

Is y equals x-3 a function?

y = x - 3 is a linear function where for each x-value we find one and only one y-value.

2x equals -3y plus 10?

2x = -3y + 10

3y = -2x + 10

y = -(2/3)x + 10

The graph is a straight line, with [slope = -(2/3)], passing through the point [ y=10 ] on the Y-axis.

Who discovered the number infinity?

Infinity was first described in India. It was first described in Isha Upanishad from India that dates back to 2nd millennium BCE as in the following verse.

Om purnam-adah purnam-idam; purnaat purnam-udacyate.

purnasya purnam-aadaaya,

purnam-Eva-avashishyate

The literal translation:

That is infinite, this is infinite;

From That infinite this infinite comes.

From That infinite, this infinite removed or added;

Infinite remains infinite.

How do you make y a function of x?

You have Y and you have X. F=function. Y is already a function of X because here's another way you write Y: F(X). So instead of putting Y you out F(X) which meanf "F or X" or "function of X".

2y equals 4 solve for y?

2y = 4 (divide both sides by 2 to solve)

y = 2

How do you find X and Y intercepts of -4X plus 3Y equals 10?

Put 0 in for x and solve for y to find the y intercept. Put 0 in for y and solve for x to find the x intercept.

-4(0)+3y=10

y=10/3

y intercept is (0,10/3)

-4x+3(0)=10

x=-10/4

x intercept is (-10/4,0)

What would x is greater than or equal to negative six look like as a graph?

At negative six on the x-axis, draw a vertical line. That line will be a solid line because we have that x is greater than OR EQUAL TO negative six. Then shade the right half of the graph -- which is where x has a value that is to the right (greater than) negative six

How do you graph x2-12x 40?

The graph of a quadratic function is y = ax + bx + c or y = a(x - h) + k, where (h, k) is the vertex.

Since x2 - 12x + 40 cannot be factored, then I will complete the square which will give me the vertex. So I will draw the parabola (which opens upward) by using the vertex and the y-intercept, (0, 40).

y = x2 - 12x + 40 add and subtract 62

y = x2 - 12x + 62 - 36 + 40

y = (x - 6)2 + 4 so the vertex is (6, 4) which shows that the parabola does not intersect the x-axis.

Since the axis of symmetry is x = 6, and the y-intercept point is (0, 40), I have another point (12, 40). I can also find other points by letting x to be 2, or 3, or 4 and finding the corresponding y-values. For example, if x = 3, then y = 13. So the point (3, 13) will give me its symmetric point (9, 13), and so on. Thus, I can use all these points to draw the parabola.

How do you find the solution of 2x equals 4?

Divide both sides by two. x = 2

2x=4

2x/2=4/2 2x/2=1x=x 4/2=2

x=2

A equals P plus PYT solve for Y?

A = P + P Y T

Subtract 'P' from each side:

A - P = P Y T

Divide each side by PT :

Y = (A - P) / PT

How do you graph -2y equals 6?

-2y = 6 so y = -3

This is a horizontal line at a height of -3 units ie 3 units below the x-axis.