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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
No - because it can be represented as a ratio :
5.2 = 520/100 = 52/10 = 26/5 etc.
Any number that can be represented as a ratio of 2 integers is classified as a rational number (other than that you can't use 0 for the denominator)
What is the derivative of ln1 divided by x?
Given y=ln(1/x)
y'=(1/(1/x))(-x-2)=(1/(1/x))(1/x2)=x/x2=1/x
Use the chain rule. The derivative of ln(x) is 1/x. Instead of just "x" inside the natural log function, it's "1/x". Since the inside of the function is not x, the derivative must be multiplied by the derivative of the inside of the function.
So it's
1/(1/x) [the derivative of the outside function, natural log]
times
-x-2=1/x2 [the derivative of the inside of the function, 1/x]
This all simplifies to 1/x
So the derivative of ln(1/x) is 1/x
What is the polynomial in descending order for 12x2 plus 20x - 25?
12x2 + 20x - 25 IS a polynomial that factors into (2x + 5)(6x - 5)
How do you solve x plus y equals 9?
In a problem where you are given two letters to add, subtract, multiply, divide, ect, you can put in any number you want for the letters. The only rule is that the two numbers must equal the number given.
For Example:
X=4 Y=5
X=3 Y=6
X=2 Y=7
X=1 Y=8
X=9 Y=0
X=10 Y=-1
x2 - (-b/a)x + (c/a) = 0 or
x2 - (sum of the roots)x + (product of the roots) = 0
Let the roots be r1 and r2. So we have:
r1 + r2 = 5
(r1)2 + (r2)2 = 15
r1 = 5 - r2 (express r1 in term of r2)
(5 - r2)2 + (r2)2 = 15
25 - 10r2 + (r2)2 + (r2)2 = 15
2(r2)2 - 10r + 25 = 15 (subtract 15 to both sides)
2(r2)2 - 10r + 10 = 0 (divide by 2 to both sides)
(r2)2 - 5r + 5 = 0 (use the quadratic formula)
r2 = [-b + &- sq root of (b - 4ac)]/2a
r2 = {-(-5) + &- sq root of [(-5)2 - 4(1)(5)]}/2(1) = [5 + &- sq root of (25 - 20)]/2 = (5 + &- sq root of 5)/2
r1 = 5 - r2
r1 = 5 - (5 + &- sq root of 5)/2
Thus, when r2 = (5 + sq.root of 5)/2, r1 = (5 - sq.root of 5)/2 or vice versa.
Since the given equation is x2 + bx + c = 0, a = 1, then c equals to the product of roots.
So that,
c = (r1)(r2) = [(5 - sq.root of 5)/2][(5 + sq.root of 5)/2] = [52 - (sq.root of 5)2]/4 = 5
Is x pluse y equals 7 direct or inverse variation?
Inverse: as x increases so y diminishes and vice-versa.
A={(6,5),(5,6)} And The probability P(A) equals1/8
3x plus y equals 6 what does y equal?
That's going to depend on the value of 'x', and it'll change every time 'x' changes.
Whatever number 'x' happens to be at the moment, 'y' equals 6 more than
triple the negative of that number.
What are the solutions to x plus 4 equals 2?
x+4=2
x=2-4 (taking 4 to other side )
x=-2
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substituting x=-2
x+4=2
-2+4=2
2=2
8x+5=5+6x
1. Get variables on the same side by subtracting 6x from both sides.
8x-6x+5=5+6x-6x
2x+5=5
2. Move all the constants to the side opposite of the variable side. (5 is a constant. Any value without an x.)
2x+5-5=5-5
2x=0
3. Get the x by itself by dividing both sides by 2.
2x/2=0/2
x=0
Your final answer is x=0
