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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 answer to x over x plus 4 equals 4 over x plus 4 plus 2?
x/(x + 4) = 4/(x + 4) + 2
(x - 4)/(x + 4) = 2
x - 4 = 2x + 8
-x = 12
x = -12
How do you factor x squared minus 25 y squared?
This is a special kind of expression called a difference of squares. Anything in the format a2 - b2 can be factored out as (a + b)(a - b). So we can say:
x2 - 25y2
= x2 - (5y)2
= (x + 5y)(x - 5y)
How can you tell when you are going to graph and Ellipse?
ax^2+by^2=k is an ellipse this is not in standard form which is x^2/a^2+y^2/b^2=1 but you will often see ellipses written this way. ellipses are also commonly written in their parametric form which is x=ccos(t) and y=dsin(t). finally a circle is a special case of an ellipse and if a b or k are 0 or negative it is not an ellipse. c and d can be positive but not 0.
How do you write an equation with 2 ordered pairs?
well its very simple
ordered pair also = coordinate
(2,3)xb=e
using variations
How do you integrate of e power 2x plus e power minus 2x?
int[e(2X) +e(- 2X)]
integrate term by term
1/22 e(2X) - 1/22 e(- 2X) + C
(1/4)e(2X) - (1/4)e(- 2X) + C
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How to make the infinity sign?
Clever to put that question here. There are a couple of ways to do it. Use the program character map in window and select font - Arial or New Times Roman. Find the ∞ symbol and copy it. Or you can use the ALT method. Hold ALT and press 0236 on your NUMERIC keypad and it will also type it. If you are using a laptop, you have to use the numbers printed over the letters uiojklm. But you can also just copy from here and paste where you need it.
∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞
How do you graph y plus 5 equals 0?
This is a horizontal line, 5 units below the x-axis (at y = -5). Since y = -5 for all x, adding 5 will give zero.
What is the slope of 9x plus 18y equals 36?
9x+18y = 36
18y = -9x+36
y = -1/2x+2 which is now in slope intercept form the slope being -1/2
Explain how you know that y must decrease when x decreases?
First you have to tell me what equation you are using as the basis of this relationship between x and y.
Is it possible to factor x2 plus 6x plus 18?
The question is equivalent to asking if there are two numbers whose sum is 6 (the coefficient of x) and whose product is 18 (the constant term). Since there are no such real numbers, the answer is NO. There is a solution in the complex domain but the normal context for such questions is the real numbers.
you take the radius and multiply it by itself. then you multiply the radius squared by 3.14 to get the area of a circle...
What is the product rule for derivatives?
If this is a homework assignment, please consider trying to answer it yourself first, otherwise the value of the reinforcement of the lesson offered by the assignment will be lost on you.
The product rule for deriviatives is d/dx f(x)g(x) = g(x) d/dx f(x) + f(x) d/dx g(x).
Think about it. You treat this as two partial deriviatives, one with f(x) and the other with g(x). In each case, the alternate is treated as constant, and can be pulled out of the deriviative. Yes, I know, partial deriviatives is part of multi-variate calculus, which is second year, but I'll leave the first year proof to the reader.
The gradient of the line is y equals -4 x plus 3 is?
When equation of line is y=-4x+3,
Gradient is -4 (as seen from the coefficient of x) and the y-intercept is +3 (point where x=0)
How many solutions does x plus y equals 4 and 2x plus 2y equals 8 have?
Infinite, both equations are equivalent and all possible solutions can be represented on the graph y = 4 - x
