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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
2x2 + 6x - 1 = 0
(-6 +/- sqrt (36 - 8)) /4
( -6 +/- 5.29) / 4
-1.5 +/- 1.32
-2.82 or -0.18
What is x to the third power plus 5x to the second power plus 2x take away 8?
x3 + 5x2 + 2x - 8
It's a third-order polynomial in 'x'.
Its value depends entirely on the value of 'x', and whenever 'x' changes,
the value of the whole polynomial instantly changes.
The general form of a quadratic expression is given as ax2+bx+c where "a" cannot equal zero and "b" is the coefficient of the variable "x" and also the sum of the factors of "c" when "a" is unity.
Example:
x2+5x+6 = (x+2)(x+3) when factored
Infinity means some non-zero value divided by zero.
It was commonly written as 1/0
Which of thw following points are on the line given by the equation y equals -3x plus 5?
(1,2)
(0,5)
(-1,8)
(2,-1)
(-2,11)
All of these are solutions to the given equation.
What is the time period of simple pendulum if its length is 100 cm?
Calculus was start from the Greek Mathematicians. They started calculating the rise and run (slope) of curves and non straight lines.
Zeno of Elea in 455 BC, discovered the concept of Infinity.
Further contributions were made by Leucippus, Democritus, Antiphon and Eudoxus.
Archimedes, was the first important person who showed advance to show that the area of a segment of a parabola is 4/3 the area of a triangle with the same base and vertex and 2/3 of the area of the circumscribed parallelogram.
Among other 'integrations' by Archimedes were the volume and surface area of a sphere, the volume and area of a cone, the surface area of an ellipse, the volume of any segment of a paraboloid of revolution and a segment of an hyperboloid of revolution.
Other important contributors were Huygens, Leibniz, Newton, Jacob, Johann, and many more.
The father of Calculus in 19th Century is Cauchy, who completed the calculus and made the shape which today we see.
-4 - 3x = 7x - 6
Add 6 to each side:
2 - 3x = 7x
Add 3x to each side:
2 = 10x
Divide each side by 10:
x = 2/10 = 0.2
7x -3 = 5x + 1 solve for x
add three to both sides
7x = 5x + 4
subtract 5x from both sides
2x = 4
divide both sides by 2
x = 2
How do you find the solution to x2-4y2 equals 16 and 2y-x equals 2?
x2 - 4y2 = 16
∴ (x - 2y)(x + 2y) = 16
2y - x = 2
∴ x = 2y - 2
∴ ([2y - 2] - 2y)([2y - 2] + 2y) = 16
∴ (y - 1 - y)(y - 1 + y) = 16
∴ -1(2y - 1) = 16
∴ 1 - 2y = 16
∴ -2y = 15
∴ y = -7.5
2y - x = -2
∴ -15 - x = -2
∴ x = -13
So the point of intersection is (-13, -7.5)
Since both are variable, you need to plug in what the values are given in the problem, then subtract y from x.
If the answer is zero , then they are equal.
If the answer is a positive number then x is greater than y.
If the answer is a negative number then y is greater than x.
4y2+16y+16=0
Divide by 4 on both sides: y2+4y+4=0
Factorise: (y+2)(y+2)=0
Therefore y= -2
What do you use cubic meters and cubic centimeters for?
Describing the volume or capacity of spaces or containers.
