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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
6x - 7 = 2x + 13
Subtract 2x from each side ==> 4x - 7 = 13
Add 7 to each side ==> 4x = 20
Divide each side by 4 ==> x = 5
What is55 over 100 in simple form?
55/100
factor out a 5
5*11/5*20
5 can be eliminated as a common factor in both numerator and denominator
11/20
======simplest form
What is the difference in meaning between f and f x?
Usually very little.
f(x) simply denotes the function f except that with this notation it is explicit that f(x) is a function of the variable x (and only x).
So, f = x + 3 and f(x) = x + 3 are equivalent.
However, there will be times, with functions of more than one variables where you wish to consider only one of the arguments while holding the other argument constant.
What are three two digits numbers that round to the nearest ten?
71 rounds to 70
75 rounds to 80
79 rounds to 80
It requires that f(a)=f(b) where a and b are beginning and ending points. Also, it says there is a c between a and such that f'(c)=0. If f were not differentiable on the open interval, the statement f'(c)=0 would be invalid.
Y equals x plus 6 and Y equals -2x minus 3 using substitution?
y = x + 6
y = -2x - 3
First we'll solve for y.
We need to get x by itself.
y = x + 6
Minus the 6, so:
y - 6 = x
Substitute x for (y - 6) and Solve the second equation (y = -2x - 3)
y = -2(y - 6) - 3
Distribute the Negative 2 to the y and -6
The two negatives become a positive 6. The y becomes negative 2y.
y = -2y + 12 - 3
Add the -2y to other y, and do 12 - 3
3y = 9
Divide out the 3
y = 3
Now solve for x, using the first equation. Replace the y for (3) and solve.
y = x + 6 when the y is substituted...
3 = x + 6
Minus the 6
-3 = x
Check your work:
Replace the y for (3) and x for (-3). Make sure it works.
y = x + 6 when substituted is..
3 = -3 + 6
Add -3 and 6
3 = 3
TRUE.
Now do the second equation
y = -2x - 3 when substituted is...
3 = -2(-3) - 3
Multiply -2 and -3 to get positive 6
3 = 6 - 3
Minus 3 from 6 to get 3
3 = 3
TRUE
X = -3
Y = 3
Can you solve x2 plus 2x - 63 equals 0?
x2+2x-63 = 0
When factorised:
(x-7)(x+9) = 0
Therefore: x = 7 or x = -9
Do you mean
y2=x2-12x+17
Well you take the square root from both sides to get y by itself.
-4x-4y equals -8 what is x and y?
There are an infinite number of (x,y) pairs that satisfy the equation.
Here are a few of them:
X . . Y
-4 . . 6
-3 . . 5
-2 . . 4
-1 . . 3
0 . . . 2
1 . . . 1
2 . . . 0
3 . . . -1
4 . . . -2
Since there are two variables, it takes two equations to pin them down.
What is inverse of a function?
Simply stated, the inverse of a function is a function where the variables are reversed.
If you have a function f(x) = y, the inverse is denoted as f-1(y) = x.
Examples:
y=x+3
Inverse is x=y+3, or y=x-3
y=2x+5
Inverse is x=2y+5, or y=(x-5)/2
How do you find the integral of tanx?
∫ tan(x) dx =
∫ sin(x)/cos(x) dx
Let cos(x) = u
Therefore, sin(x) = -du/dx >>>> (Derivative of cos(x))
∫ (-du/dx)/u dx >>>>>>>>>>> Substitute the values
∫ -du/udx dx
∫ -du/u >>>>>>>>>>>>>>>>> dx * 1/dx cancel each other out
∫ -1/u du
= -ln(u) + C
= -ln(cos(x)) + C >>>>>>>>>>> Substitute cos(x) back into u
K is known as the rate coefficient, or the rate constant. The value of k is particular, and varies from reaction to reaction. It is dependent on different factors such as temperature, pressure, concentration, solvent, presence of a catalyst, etc., and therefore a change in any of these gives you a new value for k. To determine the value of k, you must use the experimental data to determine if you have a zeroth order, first order, or second order reaction. As indicated by the equation below, you must also have the actual rate.
Rate= k[A]m[B]n[C]p
Your overall reaction order is given by the sum of the orders of reactant.
If you have a zeroth order reaction overall, then k will be equal to the rate. So if the reactants are consumed at a rate of 1.00 mol/liter/sec, then your k has a value of 1.00 mol/liter/sec. This means that no matter how much of the species you add, a lot or just enough, you will not change the rate.
If you have a first order reaction where the concentration of A, [A] (in mols/liter), is consumed at a rate of .004 mol/liter/sec, then k = [A]/.004 mol/liter/sec, as given by the above equation: You divide the rate by the concentrations of the reactants. The units for a first order reaction are sec-1 or 1/sec, because you are dividing moles per liter by moles per liter per second. So the concentration of this does matter. The concentration of the reactant is proportional to the rate of reaction.
If you have a second order reaction, then the addition of a reactant will increase the rate of reaction by a square of the concentration of the reactant. This is because you are now dividing the rate of reaction by, for example, [HNO3]2. Remember the the previous variables m, n, or p are the experimentally determined order of reactant. So a second order reaction results in squaring the concentration. Hope that helps!
Which of the following methods would be the easiest to use to solve x2 - 6 equals 0?
x^2-6=0x^2=6
x=±√6
What is the answer do this matrix in arbitrary form 3x-6y-z equals 6 and x plus y plus 3x equals 5?
It is a singular matrix.
How does the graph of y equals x2 differ from the graph of y equals x2-4?
Assuming you meant y=x2 & y=x2-4
They are both straight-line graphs, however - they produce different results. Using the values of 1,2,3,4 & 5 for x (as an example)...
In the first equation, the value of y would be 1,4,8,16 & 25
In the second equation, y would be -3,0,4,12 & 21
