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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 integral of 2 1-x dx with limits 0 to t?
I think you meant the integral of 21-x dx, or as I write it ,/`21-x dx.
Use u-substitution where u = 1 - x. Note that the derivative of this equation is du = -1 dx, so we know dx = - du.
Rewriting the original integral in terms of u, integrating, then putting it back in terms of x gives us:
,/` 21-x dx
,/` 2u (-du)
- ,/` 2u du
- 2u / ln(2)
- 21-x / ln(2)
Note that the second to last line can be found in any integral table, and ln denotes natural log.
Now the bounds go from x = 0 to x = t, so:
[- 21-t / ln(2)] - [- 21-0 / ln(2)]
- 21-t / ln(2) + 2 / ln(2)
(-21-t + 2)/ln(2)
How do you solve 2x plus 6x minus 3 equals 13?
2X + 6X - 3 = 13
add 2X and 6X together
8X - 3 = 13
add 3 to each side
8X - 3 + 3 = 13 + 3
8X = 16
divide both sides integers by 8
(8/8)X = 16/8
X = 2
----------------check in original equation
2(2) + 6(2) - 3 = 13
4 + 12 - 3 = 13
13 = 13
checks
Why is a summation greater than an integral?
It's not. It depends on the method you use for summation whether
summation > integral
or
integral > summation.
3x=9 means 3 times a number is equal to 9.
Divide both sides by 3.
1) 3x/3=9/3
Dividing 3x by 3 cancels the 3 from the x.
2) 3x/3=9/3
Cleaning up the equation looks like this:
3) x=9/3
Solve the right side.
4) x=3
8 - x + 14 = 16x
We first attempt to isolate the variable and simplify the statement:
22 = 17x
Divide by 17, yielding only 'x'.
22/17 = 1 5/7
Suppose y varies directly with x and y equals 12 when x equals 6write an equation realting x and y?
y = kx ie y/x = k, k = 2, so y = 2x
What is the value of x if 7 divided by 2x equals 3?
7/2x = 3
Multiply both sides by 2x: 7 = 3*2x = 6x
Divide both sides by 6 = 7/6 = x ie x = 1.1666...
How do you write P x 9 x 3 x Q x P x 9 in exponential form?
92(P2Q) or 81(P2Q) is the best you can possibly do.
Which direction would the graph of yx plus 2 plus 3 open?
It is not possible to answer the question because there is no equation - only an expression.
What is x in the equation -9-6x plus 7x equals 1?
x=10
For the equation -9 - 6x +7x = 1
First, add nine to both sides to get all of the x's on one side
-9 - 6x + 7x = 1
+9 +9
-6x +7x = 10
Then, combine like terms on the left side
-6x+7x=10
x=10
How do you solve g x equals -3x plus 1?
If: x = -3x+1
Then: x+3x = 1 => 4x =1
So: x = 1/4 or 0.25
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I notice that the question requests a solution for g x = -3x + 1.
It seems possible that parentheses around the 'x' after the 'g' have gone missing, along with a prime indicating the derivative of the function g. This being the case, we would be seeking the antiderivative of -3x + 1.
The antiderivative of a sum is the sum of the antiderivatives. So we can look at -3x and +1 separately.
The derivative of x2 is 2x. Therefore, the antiderivative of x is x2/2, and the antiderivative of -3x is -3x2/2.
The antiderivative of 1 is x.
Overall, the solution is the antiderivative -3x2/2 + x + C, where C is an arbitrary constant.
What is 3x4 plus 5x3 plus x2 - 5 divided by x 2?
3x4 plus 5x3 plus x2 - 5 divided by x 2 =[(3x4) + (5x3) + (x2 - 5)]/x2 =
(12 + 15 + x2 -5)/x2 =
(27 - 5 + x2)/x2 =
(22 + x2)/x2
What I mean by this equation is:
x^3-2x^(x-2.5)+x^(x^x)
