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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 physical name for fourth order derivatives?
We call "jerk" the third order derivative of position with respect to time, that is, the variation of acceleration. Some say that the derivative of jerk with respect to time (the fourth derivative of position with repsect to time) is called "jounce" or "snap".
What does ahead of the curve mean?
Anticipating issues and able to resolve them ahead of time; above the averaged baseline of expectations or requirements.
What is the difference between integration and derivation?
Integration results in an equation which gives the area under the original equation between the bounds. Derivation results in an equation which gives the slope of the original line at any point.
False.
What is X plus 1 divided by 3y equals -11 and 3x divided by 4-y divided by 2 equals -15?
Your equations are not worded properly.
What is the strategy for finding the cube root of complex numbers?
Here's how you can find any power (fractions would be a root of a number) of any number (complex or real). A real number is a subset of the complex number set, with the imaginary part = 0. I'll refer you to a related link on Euler's formula for information about how this is derived. A complex number can be graphed on the Real-Imaginary plane, with reals on the horizontal axis, and imaginary on the vertical. Convert the complex number from x-y style coordinates in this plane to polar coordinates.
For a complex number a + bi, here's how you do that. We will end up with a magnitude and an angle. The magnitude is sqrt(a² + b²). The angle is found by tan-1(b/a). Now to find a power, apply the power to the magnitude (for cube root this is exponent of 1/3). Then multiply the angle by the power (in this case you divide by 3). Really for a cube root there will be 3 distinct roots. Since a the angle of a circle is 360° or 2pi radians, you can add 2pi radians to the angle of the original complex number, then divide by 3 to determine the second root. Add 4pi radians to the original angle and then divide by 3 to determine the 3rd root. Then convert back to x-y coordinates if you want to:
Magnitude*(cos(angle) + i*sin(angle)), for each of the 3 angles that you determined.
See the question: 'Strategy for finding the cube root of complex numbers'
What is a degree in a differential equation?
A degree of a differential equation is the highest power of highest order of a differential term of the equation.
For example,
5(d^4 x/dx^4) - (dx/dx)^2 =7
Here 5(d^4x/dx^2) has the highest order and so the degree will be it's power which is 1.
How are integers used in the real world?
integers are number
It's used in banks, thermometers, it's whole number that is negative! It's very important to know.
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If this has something to do with school, then I would say integers are easy, and important. If they seem hard for you (as you obviously think they're useless), then study more, you'd benefit from it, and use it "in the real world".
How do you answer 9x equals 12x-9?
9X = 12X - 9
subtract 12X from each side
-3X = -9
divide each side by -3 ( remember, dividing negative by negative number = positive number )
X = 3
check
9(3) = 12(3) - 9
27 = 27
checks
3y-x equals 0 and 2x plus 2y equals 7?
Multiply First equation by 2: 6y - 2x = 0
Add second equation to this: 6y - 2x + 2x + 2y = 0 + 7
Simplify: 8y = 7 so y = 0.875 and x = 2.625
Can spreadsheets be helpful with advanced math areas like algebra and calculus?
Yes. I use them a lot when answering these questions.
What is difference between oscillatory and simple harmonic motion?
Simple harmonic motion (SHM) is in one dimension whereas oscillatory motion is 2-dimensional motion that is SHM in one dimension but linear in another.
Simple harmonic motion (SHM) is in one dimension whereas oscillatory motion is 2-dimensional motion that is SHM in one dimension but linear in another.
Simple harmonic motion (SHM) is in one dimension whereas oscillatory motion is 2-dimensional motion that is SHM in one dimension but linear in another.
Simple harmonic motion (SHM) is in one dimension whereas oscillatory motion is 2-dimensional motion that is SHM in one dimension but linear in another.
Importance of fundamental duties?
The importance of fundamental duties is that they define the moral obligations of all citizens to help in the promotion of the spirit of patriotism and to uphold the unity of India. However , they are not legally enforceable.
What is the second derivative of the square root of x to the power of 3?
3/(4*square root(x))
....Mukesh
How do you graph absolute value of x minus absolute value of y equals 1?
Graphs are difficult to describe here but let's try. If x is 1, then y is 0. Start with point (1,0). If x is 2 then y is one. (2,1). There is a line starting at 1,0 and going up and to the right with a slope of one.
But, if x is 2, y could also be -1 because the absolute value of -1 is 1. There is another line starting at 1,0 and going down and to the right with a slope of -1.
Then, if x is -1, y is also zero. Start again with point (-1, 0). Without showing a lot of detail, the left side of the graph is a mirror image of the right side. When you are done your graph should look at bit like > < .
Which line represents 5x plus 4y equals 20?
5x+4y=20 is technically the equation of a line.
A more familiar representation of the line is in "y equals" notation. This simply means that the y variable has been isolated (this notation is usually required for graphing calculators). To get the equation in y equals notation, simply isolate the y variable:
5x+4y=20
4y=(-5)x+20
y=((-5)x+20)/4
What does twice differentiable mean in calculus?
eg. If y = x^5 (^5 means to the power of 5).
Then y' = 5x^4 (i.e. differentiating once)
Then y'' = 20x^3 (differentiating twice)
An antiderivative, F, is normally defined as the indefinite integral of a function f. F is differentiable and its derivative is f.
If you do not assume that f is continuous or even integrable, then your definition of antiderivative is required.
