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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
Assume you want to know what is the formula of the gradient of the function in multivariable calculus.
Let F be a scalar field function in n-dimension. Then, the gradient of a function is:
∇F = <fx1 , fx2, ... , fxn>
In the 3-dimensional Cartesian space:
∇F = <fx, fy, fz>
What is the use of successive differentiation?
There are several uses.
For example:
* When analyzing curves, the second derivative will tell you whether the curve is convex upwards, or convex downwards.
* The Taylor series, or MacLaurin series, lets you calculate the value of a function at any point... or at least, at any point within a given interval. This method uses ALL derivatives of a function, i.e., in principle you must be able to calculate the first derivative, the second derivative, the third derivative, etc.
How do you graph the equation y equals -1?
y=-1
No matter what value x has, y is always -1, so the graph is a horizontal line passing through (x,y)=(0,-1).
What is y equal x and y equal x plus 2?
That is irrelevant, there is not possible way y=xy, and there is no possible way xy=x.
Does the suspension material affect the period time of a pendulum?
No. Period does not depend on the suspending material. Since the expression derived is:
T = 2Pi(l/g)-1
Of course we rely on some conditions.
1) the string is torsion less
2) the amplitude of oscillation is to be small
3) some massive material is to attached so as to keep the string under tension.
How do you evaluate f x equals 3x plus 2 at f 2?
if f(x) = 3x + 2 and you're looking for f(2), just plug in 2 for x: f(2) = 3(2) + 2 = 6 + 2 = 8.
How do you find the intercepts to the equation x2 plus y-49 equals 0?
x2 + y - 49 = 0
At the x-intercepts, y=0:
x2 - 49 = 0
(x+7)(x-7) = 0
x = -7 and x = +7
At the y-intercept, x=0:
y - 49 = 0
y = 49
General Solution
set x=0 to find your y-intercept and set y=0 to find your x-intercept. That's how you will always find your intercepts, no matter what the equation is.
Ex. So if you find that when x=0, y=a, then the y-intercept is at the point (0,a).
Similarly, if you find that when y=0, x=b, then the x-intercept is at the point (b,0).
You can solve any problem from here.
When you find particular integral then why you not add constantof integration?
Where you refer to a particular integral I will assume you mean a definite integral. To illustrate why there is no constant of integration in the result of a definite integral let me take a simple example. Consider the definite integral of 1 from 0 to 1. The antiderivative of this function is x + C, where C is the so-called constant of integration.
Now to evaluate the definite integral we calculate the difference between the value of the antiderivative at the upper limit of integration and the value of it at the lower limit of integration:
(1 + C) - (0 + C) = 1
The C's cancel out. Furthermore, they will cancel out no matter what the either antiderivatives happen to be or what the limits of integration happen to be.
How do you graph 8x plus y equals 4?
8x + y = 4
First you have to get the y by itself. So you minus 8x from each side because you need positive y.
New equation: y=-8x+4
Next you need to make some co-ordinates.
So, (-3,28), (-2, 20), (-1, 12), (0, 4), (1, -4), (2, -12), (3,-20)
Plot these on your graph.
I hope this helps
Solve for x rounding to the nearest 100th 7x equals 12?
7x = 12
Divide each side by 7:
x = 12/7 = 1.71 (rounded)
How would you graff x plus y equals -3?
Graph any two numbers that add together and get -3. Like, (5,-8) (0,-3) and then draw a line through them.
Can equation and inequality have the same solution?
No, inequalities have more than, less then, at least, or no more than signs. Equations just have equal signs. An inequality answer can't be written as just a number it has to have a sign with it.
How do you Solve 3x2 plus 3x - 2 equals 0 using discriminant?
D = 33.So the solutions to 3x^2 + 3x - 2 = 0 are
x1 = [-3-sqrt(33)]/2*3 = approx -1.4574, and
x2 = [-3+sqrt(33)]/2*3 = approx 0.4574.
68-3x=10x+16
Combine like terms. (Subtract 16 from both sides. Subtract -3x from both sides.)
This will give you: 52=13x
Divide both sides by 13. Your answer is x=4.
What is the amplitude of y equals 4 sin 3x?
'Y' varies between -4 and +4. Viewed as a wave, its amplitude is 4.
a line that has a Y-intercept of 9 and goes up four for ever one it goes right.
Rise: 4
Run: 1
Y-intercept: 9
The 3D volume is 8s^3. The 4d "Volume" is s^4.
Btw, why do you need to know this. It took me years to figure this, and more, on my own...
