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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 can you write a function that represents all possible antiderivatives of a given function?
Given a function f(x) find any anti-derivative, F(x). The set of all possible derivatives is obtained by adding a term not involving x which can take any value.
So F(x) + C is a general derivative, where C can take any value.
y = f(x) = 2x2 - 3x + 10
dy = (4x - 3) dx
Note:
It's possible that the function in the question may have been f(x) = (2x)2 - 3x + 10 .
If that's the case, then
dy = (8x - 3) dx
2 divided by x plus 4divided by 3 equals 2?
(2/x) + (4/3) = 2
Multiply each side of the equation by 'x':
2 + 4x/3 = 2x
Multiply each side by 3:
6 + 4x = 6x
Subtract 4x from each side:
6 = 2x
Divide each side by 2:
3 = x
5X + 7 = 42
subtract 7 from each side
5X + 7 - 7 = 42 - 7
5X = 35
divide both sides integers by 5
(5/5)X = 35/5
X = 7
----------check in original equation
5(7) + 7 = 42
35 + 7 = 42
42 = 42
--------------checks
2x minus 3y equals 11 5x plus 2y equals 18?
Presumably this is a simultaneuos equation question that can be solved using the elimination method:
2(2x-3y = 11)
3(5x+2y = 18)
Multiply all terms in the top equation by 2 and in the bottom by 3:
4x-6y = 22
15x+6y =54
Add both equations together:
19x = 76
Divide both sides by 19 to find the value of x:
x = 4
Substitute the value of x into the original equations to find the value of y:
Therefore: x = 4 and y = -1
1000000000*2.6 = 2600000000 or, more simply, 2.6*109 or 2.6 billion.
Does a differentiable function have to have a relative minimum between any two relative maximum?
Yes.
What is the y value of y equals -x2 plus 2x?
That's going to depend completely on the value of 'x'.
There are an infinite number of things it could be.
