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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
How do you i find the arc length of The equation is 3x43 - 332x23 from -27 to 216?
Please clarify the equation. It does not make sense.
In the hope that it might answer your question, I will determine the length of the curve (hereinafter length) y=3x^43-332x^23 from x=-27 to x=216. length=integral from -27 to 216 of √(1+(129x^42-7636x^22)^2)dx. Solve this by Google searching "definite integral calculator", then clicking on the first result, which should be wolframalpha. Plug in the values there and you will have your answer!
Is the number 0 a complex or real number?
It is a real number because for example water freezes at 0 degrees Centigrade
How do you graph y equals 2x plus 13?
first of all, y=2x + 13 is in the form of y= mx +b, so all you do is go up 13 units vertically on the coordinate plane and plot a point. Second, because m is your slope and 2 is in the place of the m, go up two vertically and over right one horizontally.
How many 4 number combinations can be made from four numbers?
If repetition is allowed and order is important, then you have essentially a base-4 number system, with the numbers ranging from 00004 to 33334. The quantity of permutations in this example is 44 = 256. If repetition is not allowed, but order is important, then it is 4! = 24.
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The above answer is perfectly correct. But, as stated in the answer, for permutations. However, according to the mathematical definition of combinations (as opposed to permutations), the order is irrelevant to combinations. 1234 is the same as 1423 or 4213 etc. Consequently, there can be only one 4-number combination from 4 numbers
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 does 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 equals?
Either 10000000000, 10^(10) or ten billion. Depending on how you wish the answer to be
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 answer to 3x plus 14x plus 8 equals 0?
First of all ... let's make sure you understand what the question is. With examples like
that one, the question is usually: "What value of 'x' makes the statement true ?" .
3x + 14x + 8 = 0
Combine like terms:
17x + 8 = 0
Subtract 8 from each side:
17x = -8
Divide each side by 17:
x = -8/17
That's the only value of 'x' that makes the original statement true.
In case you meant 3x2 + 14x + 8, that factors to (x + 4)(3x + 2)
x = -4, 2/3
It will half.
How can you Solve this problem by substitution 6X- Y equals -9 4 plus 7X equals -Y?
We have two equations.
6x-y=-9 and -y=7x+4.
We substitue 7x+4 into the first equation and we have
6x+7x+4=-9 or 13x=-13 so x=-13/13 of -1
Now plug that into either equation and we have
-y=-7+4 or -y=-3 so y=3.
The solution is (-1,3)
X such that x is an element of I x is equal to or more than 3 what does the I stand for?
The I stands for 'Integers' (in this case the answer is {3, 4, 5, 6, ...}).
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
