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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 double integral of 2x?
The integral of a single term of a polynomial, in the form of AxN is (A/N+1) x (N+1).
The first integral of 2x is x2 + C.
The second integral of 2x is the first integral of x2 + C, which is 1/3x3 + Cx + C.
18360 WHAT a dumb question you could have did it your self . On a calulator
sIGNing by: Back pack
0.5(x)+3=9
First you subtract 3 from the problem on the left side. +3 and -3 cancel out. Whatever you do to one side you do to the other so you subtract 3 from the right side to. 9-3=6.
Then bring everything else down.
0.5(x)=6
Since you still want to isolate the (x), you have to divide by 0.5 underneath the multiply by 0.5. This cancels it out. Whatever you do to one side, you do to the other. 6/.5=12
x=12
To check your answer you do the 3 (or more) step check. This check will be 4 steps.
1. Rewrite (rewrite the problem): 0.5(x)+3=9
2. Replace (plug in your answer for x) 0.5(12)+3=9
3. Solve (solve the problem (may take more than one step)): Multiply 0.5 * 12
Bring down: 6+3=9
4. Compare (compare what you got on the left with what if on the right): 9=9
Yes! 9 equals 9! We got it right! The answer is 12.
∫ f'(x)g(x) dx = f(x)g(x) - ∫ f(x)g/(x) dx
This is known as integration by parts.
Can two numbers having the sum of 6 be repersented by x and x plus 6?
No. The sum of (x) and (x+6) is (2x + 6), not 6.
What you want is (x) and (6 - x). The sum of those two is always 6, no matter what 'x' is.
How do you solve this problem -3x plus 7y equals -1 -2x plus 5y equals 0?
-3x + 7y = -1 -2x + 5y = 0
What I would do is split the equation into two and label them:
[A] -3x + 7y = 0
[B] -1 -2x +5y = 0
Now change [B] so that the number term is on the other side (not essential, but it makes it a bit cleaner)
[B'] -2x + 5y = 1
Now you can use elimination to get rid of either x or y. I'm going to do it for x, but first you need to make the numbers on the x's the same. So we multiply all of [A] by 3 and [B'] by 2:
[A'] -6x + 14y = 0
[B''] -6x + 15y = 3
Now you can subtract one from the other and since the x terms are the same, they will cancel out. I'm going to subtract [A'] from [B''].
-6x - (-6x) + 15y - 14y = 3 - 0
so
y = 3
Then you put y back into one of the equations, for example [A]:
-3x + 7y = 0
-3x + 7(3) = 0
-3x + 21 = 0
-3x = -21
3x = 21
x = 7
hence
x = 7, y = 3
What is 21 squared x 33 sqared times 66 squared?
2,091,964,644
How to work fast (without calculator)
212* 332 * 662 = (21*33*66)2 = 457382
21*33 = 693 (easy)
693*66 = 45738
693*
066
6*3 = 18
1 + 6*3 + 9*6 = 73
7 + 6*9 + 6*6 + 0*3 = 97
9 + 6*6 + 0*9 = 45
4 + 0*6 = 4
457382 = 4252723282 = 1625490964
101*2(3*8) = 480
102*2(7*8) = 11200
103*2(7*3) = 42000
103*2(5*8) = 80000
104*2(5*3) = 300000
105*2(5*7) = 7000000
104*2(4*8) = 640000
105*2(4*3) = 2400000
106*2(4*7) = 56000000
107*2(4*5) = 400000000
1625490964+ = 2091964644
0000000480
0000011200
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0000080000
0000300000
0007000000
0000640000
0002400000
0056000000
0400000000
5y2 : the only factors are 5y and y
Similarly the only factors of 5 are 5 and 1
these figures must be arranged so that their indiviual multiples total 26y:
This can only be (5y + 1)(y + 5)
So x = -1/5 or -5
Raja was absent for the class yesterday.what is the mistake?
The question was posted several years ago so Raja was not absent from the class yesterday. He no longer goes to school!
How is discover the separations of variables?
I firmly believe that most brilliant ideas come from people just playing with things.
"Hmmm... what happens if I assume that the solution is in this form..."
How do you find the value of the discriminant -16x2 plus 10x-20 equals 0?
Calculate 10^2 - 4*(-16)*(-20)
What are three dimensions are needed to find the volume of a rectangular solid?
length, width, height
What is the significance of the x-value in a sine wave function?
The answer will depend on where, in the sine function, the x-value appears:
For example, its roles in
f(x) = sin(x), or
f(x, theta) = x*sin(theta) or
f(x, theta) = sin(x*theta)
f(theta) = sin(theta + x)
are quite different.
How do you factor x2 -2x-8 using the quadratic formula?
X2 - 2X - 8 = 0
Quadratic formula.
X = - b (+/-) sqrt(b2 - 4ac)/2a
a = 1
b = - 2
c = - 8
X = - (- 2) (+/-) sqrt[(- 2)2 - 4(1)(- 8)]/2(1)
\
X = 2 (+/-) sqrt(4 + 32)/2
X = 2 (+/-) sqrt(36)/2
X = [2 (+/-) 6}/2
X = 4
=====
How many solutions are there to the problem x equals -5y plus 5?
Infinitely many.
The solution is a pair of numbers ... one number for 'x' and one number for 'y' ...
that makes the statement [ x = -5y + 5 ] a true statement.
There are an infinite number of those pairs.
The graph if this equation is a straight line, and every point on the line is a solution to the equation.
Here are a few of them:
. Y . . . X .
-3 . . . . 20
-2 . . . . 15
-1.27 . . 11.35
-1 . . . . 10
0 .. . . . . 5
1 .. . . . . 0
2 . . . . . -5
3 .. . . . -10
4 .. . . . -15
4.73 . . -18.65
What is the solution for 9x 2 plus 0x-81 0?
The answer to this equation is the number 99. This is taught in high school math.
