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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

How do you do compositions of functions backwards?

I am not entirely sure what you mean; in general, if you change the order of composition, you will usually get different results: f(g(x)) is usually NOT equal to g(f(x)).

Where are the points of intersection of the line x -y equals 2 with the curve x2 - 4y2 equals 5 by completing the square?

If: x -y = 2 then x = 2 +y

If: x^2 -4y^2 = 5 then (2 +y)^2 -4y^2 -5 = 0

Removing brackets: 4 +4y +y^2 -4y^2 -5 = 0

Collecting like terms: 4y -3y^2 -1 = 0

Divide all terms by -3: y^2 -4/3y +1/3 = 0

Completing the square: (y -2/3)^2 -4/9 +1/3 = 0 => (y -2/3)^2 = 1/9

Square root both sides: y -2/3 = -1/3 or +1/3

Add 2/3 to both sides: y = 1/3 or 1

By substitution into original equation intersection are at: (7/3, 1/3) and (3, 1)

What is 6 plus 17y equal 15 plus 14y?

If: 6+17y = 15+14y then 17y-14y = 15-6 so 3y = 9 and then y = 3

Why is ddx the derivative operator for Calculus?

It is the operator used by Gottfried Liebniz, who developed calculus (in parallel with Newton).The "d" denotes a difference and, the full representation, dy/dx (not ddx), is used to represent a change in y divided by (per) a change in x. However, calculus goes further than comparing simple changes but uses these changes for smaller and smaller changes in x, that is, the limit of the change as dx approaches 0.

Java programme to find area of a circle?

well, the formula is A=pi(r)^2 r=radius A=area ^=to the [insert number here] power pi=3.14...

What are two numbers that have a sum of 390 and a product of 34304?

Call one of the numbers x. Since the sum is 390, the other must be 390 - x. Thus we have x(390 - x) = 34304. Solving this quadratic equation, we find the numbers are

134 and 256.

What is the answer to Solve 3 x x 1 for x?

Wiki answer limits your ability to insert operators in questions, so please write out the word "equals" or "plus" as it is necessary.

Can you make a 4banger in to a v6 in an Alero and what all would it take?

Change engines. It would take a donor car and lots of work by someone who knew what they were doing. Forget going that route. Sell the 4 cylinder and buy a V6 if that is what you want.

What is the integral of x divided by a 7?

First just "factor" out the constant: (1/7)

x/7 dx = 1/7

x dx


The integral of xn is xn+1/ (n+1)
In this case, our n=1 so:
x(1+1)/(1+1) = x2/2


Don't forget about the 1/7 we factored out:
(1/7)(1/2)(x2) = x2/14


Therefore the answer is (don't forget your C):

x/7 dx =

x

2/14 + C

What is the value of x in x plus 15?

The information given places no restriction at all on the value that x can have. It can be any number - integer, rational, irrational or complex - of any magnitude.

What is the value ofx when y equals 6?

It depends on the relationship between 'x' and 'y'. That information is usually

presented in the form of an 'equation'. But you haven't given us one, so there's

no way anybody can begin to figure it out.

What is A equation for -2x plus 8 equals 7x-10?

-2x + 8 = 7x - 10 is technically an equation, in and of itself.

Can you give me area of a quadrilateral with sides measuring 197 x 39 x 196 x 42?

Not without knowing at least one of the angles.

You would need to know at least two of the angles (preferably opposite angles) then use Brahmagupta's formula.

How do you solve this problem 7x - 3 - 2x equals 17?

7x - 3 - 2x = 17

-2 -2

7x - 3 - x = 15

-7 -7

x - 3 - x = 8

+3 +3

x - x = 11

+x +x

x=11x

-x -x

(x=) 11

does that look familiar from class? You can do it different ways...

* * * * *

Yes, you can do it the correct way, instead!

7x - 3 - 2x = 17

Combine the like terms (7x and -2x) on the left side: 5x - 3 = 17

Add 3 to both sides: 5x = 20

Divide both sides by 5: x = 4

Check:

7*4 - 3 - 2*4 = 28 - 3 - 8 = 28 - 11 = 17

Does not work with x = 11!

What is the solution to 7over8b-1 equals -15over16b plus 4?

If you mean: 7/8b - 1 = -15/16b + 4

Then the value of b works out as 0.3625