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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 inverse of 15-8times x divided by 3?
y = 15 - 8x/3
y - 15 = -8x/3
15 - y = 8x/3
x = 3/5(15 - y)
and so x = 9 - 3y/5
How to solve e to the power of 3x plus 5e to the power of x equals 7?
e3x+5 x ex =7
e3x+5+x=7
4x+5=ln(7)
x=(ln(7)-5)/4
Is infinity equal to infinity?
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Infinity is a math concept. nothing in the real world is infinite (without limits). In other words, two infinities are equal only if the math teacher says so.
Infinity isn't a number or a value so you can't compare its size to another infinity.
How do you factorise x squared minus x minus 30?
x2-x-30 = (x-1/2)2 - 1/4 -30 as (a+b)2=a2+2ab+b2 with a=x then b=-1/2
= (x-1/2)2 - 121/4
= [(x-1/2)-sqrt(121/4)] [ [(x-1/2)+sqrt(121/4)] as a2-b2=(a-b)(a+b)
then = (x-1/2-11/2)(x-1/2+11/2) = (x-6)(x+5)
How is the solution set of the sentence described x plus 57?
There is no solution set. x + 57 is an expression, not an equality, nor even an inequality. An expression CANNOT be solved!
How do you solve y equals -x2 plus 3?
Set y as zero; now you have -x2+3=0.
Multiply equation by -1; now you have x2-3=0.
Add both sides by 3; now you have x2=3.
Take the square root of both sides, and finally you have the answer, which is x=±√3.
What will the graph of x equals 100 look like?
It will look like a straight vertical line that cuts the x-axis at the point (100, 0).
this question makes no sense. do you mean what are the zeros/roots of this polynomial?
Factoring trinomials are fun!
5x2 - 8x - 4
(5x + 2)(x - 2)
Never forget to check:
5x2 - 10x + 2x - 4
5x2 - 8x - 4
Good everything is in order, now set each parentheses equal to zero to solve for x
5x + 2 = 0
5x = -2
x = - 2/5
x - 2 = 0
x = 2
All done! Now we know the solution set is {-2/5, 2}. Remember smallest number always goes first.
What is the answer to 2y equals 8x-6?
This reduces to the equation y=4x-3 (by the division of all factors by 2).
What is an example of a function?
Functions basically establish relationships between expressions. Many common Algebraic functions are expressed as functions of x:
f(x) = x2 + 4
Which could also be written as y = x2 + 4
However, this just scratches the tip of the universe. Not only do mathematical functions vary in complexity and offer an infinite number of possibilities, there are also programming functions. Programming functions are typically groups of commands that accept one or more parameters, then return one or more pieces of information.
The above Mathematical function can be re-written as a Perl programming function that accepts a value for x:
sub calculateFunction {
my ($x) = @_;
my $y = x**2 + 4;
return ($y);
}
What does y represent in y equals 3x plus 5?
y is the result if you multiply x by 3 and add 5 to it. For example, if you claim that x is 1, then if you multiply x by 3 and add 5, you would get 8. This result, 8, is what y is equal to (when x equals 1).
If x plus 5x plus 3 equals 27 what is x?
6x+3=27
6x=24 (subtract 3 from each side) x=4 (divide both sides by 6)
What is the natural base of e?
'e' is an irrational number ... it can't be written completely using digits, fractions,
or decimals, so it has to be written as a symbol, just like 'pi'.
Here's the beginning of it: 2.718281828459045 . . .
'e' is a number that keeps popping up, when you do the math for any kind of process
where the speed depends on how far it still has to go to reach the finish line.
Famous example . . . Picture this: The width of your bedroom is 'W'. One morning,
you stand with your back to the wall at one side of your bedroom, and when your
Mom says 'Go', you start walking across the room to the other side, like this:
Every second, you walk 1/2 of the distance you have left.
For one thing, you'll never reach the other side, because you can only cover
1/2 of the remaining distance in the next second. But that's another story.
After 'T' seconds, the distance you have left to go is: W e-0.69T
and there's an example of how that number 'e' keeps coming up.
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My improvement to the previous answer is not an improvement to the actuall value of e previously mentioned, but another description of what e, or the value actually means: as to why 2.71828 and not some other value. I try to explain why it is then called "natural".
e or epsilon is about 2.71828 e is a very important number like PI = 3.14...
This is called a natural number because it occurs in nature alot like the Fibonacci series or numbers. e can be used to calculate natural growths and decays. For example an object that is cooling down, the temperature can be calculated where the formula for that has e in it. A series for e has been developed which has great power in finding not only powers of e but powers and roots of any value since series for those values have not been developed (such as a series for powers of 10).
The definition of e is based upon (1/1 + 1/n)^n where n is very high. Quickly though it reaches 2.718 even when n is lower. The value of this expression approaches the value of a constant we will just call e. If you have infinitely compounded growth during one period of time, the initial value will grow to about 2.718 times bigger for that entire period, and not some enormous value like some might think initially. The reason is that the compounded growth value to be added in gets very small when the number of intervals (n in the formula) of compounded growth is very high.
Because of the natural nature of e, it was chosen as a base for logarithms. When e is used, the logarithm is then often called a "natural logarithm".
In short the derivative of (ln x) is (1/x), ie. the reciprocal of that x, and then a reciprocal series (of terms to be calculated) was developed to find the natural logarithm of a number. This series for the natural logarithm of a number is very powerful since series to calculate other logarithms with different bases have basically never been developed yet. In essence, logarithms of other bases are calculated with the natural logarithm series and then the resulting value is converted or adjusted (usually with a multiplication by a value) to what is should actually be.
Another interesting fact about e, is that the derivative of e is e or itself. Likewise, the derivative of any other power of e is that same value. In short, this means that on a curve on a graph, the steepness or slope of that curve at that point is equal to that current value of e, that is, itself.
How much liquid is in a 4' x 4' x4' container?
A 4' x 4' x 4' container has a capacity of 64 cubic feet, or about 478.75 gallons. (rounded)
We have no way of knowing how much liquid is in it. For all we know, the container
may be empty, and you may just be trying to catch us with a trick question..
Where do the equations yequals7x 1 and yequals4x 2 intersect?
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "equals", "squared", "cubed" etc.
There are no operators between x and the following constant terms.
Could please differentiate 12x?
To differentiate something you multiply the power on the x with the number in front of it and then reduce the power by one
in this case:
12x is the same as 12x^1
so the derivitive is 12*1*x^0
which is just 12
