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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
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.
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)
The number 51 is not the square of a whole number. It is the square of 7.1414.
What couse should you opt after bsc maths msc maths or bed maths?
A course in spelling, or typing, obviously!
How do you solve -20 equals -4x plus 6?
-20 = -4x +6
add 20 to both sides
0 = -4x +26
4x = 26
x = 26/4 = 6.5
What is the anti derivative of e x2?
The integral of x^2:
f(x)= A . x^n
f´(x)= A . n . x^(n-1) = x^2
Hence, n must be 3 for (n-1)=2 which automatically means that A must be 1/2 in order for A . n= 1
Thus, f(x)=0,5 . x^3 (antiderivative)
0,5e . x^3
What is the x and y intercepts of -3x plus 5y equals -15?
-3x + 5y = -15
At the x-intercept, y=0:
-3x = -15 . . . . . x = 5
At the y-intercept, x=0:
5y = -15 . . . . . y = -3
How many solutions are possible for 2x equals 2y plus 2 and 2y equals 2x plus 2?
There are 0, or no solutions to these equations. If you rearrange each equation to look like an equation of a line, you will have the two lines:
y = x -1 and y = x + 1, which are two parallel lines. They do not intersect at any point, so there is no solution.
How can the graph of y equals kx be interpreted for different contexts?
It is a straight line through the origin and, if k > 0 reflects a direct relationship between x and y. This means that each unit increase in x is associated with y increasing by k.
If k < 0 it reflects a direct but negative relationship and this means that each unit increase in x is associated with y decreasing by k.
If k = 0 then the result is the x-axis. This means that changes in x are not associated with changes in y.
None of the above imply causation.
What is rage mathematically speaking?
a notation showing all of the y-values produced by the indicated function.
Domain is a notation showing all of the x-values that produce real answers.
How do you log out when playing Wizard101?
click esc on your keyboard ( which opens up your spellbook), then click quit at the bottom of the screen. when it brings you to the character selection click exit again.
If you graph this it will be a parabola that has each end pointing down. It crosses the x-axis at:
y=-2x^2+3x+5
y=-1(2x^2-3x-5)
y=-1(2x-5)(x+1)
y=5/2
y=-1
What is the step by step answer to x plus 4divided by x to the second power 12x 44?
The lack of brackets here makes it impossible to work out what this mathematical expression really is. For example "x plus 4 divided by x.." could be x + 4/x or it could be (x+4)/x .. and so further.
