0
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 are some real life application of exponents and logarithms?
Logarithms are used in the royal navy in sonars
They are but it's far wider than that.
The application you mean is the "decibel", the 10X or 20X logarithm of the ratio of two signal intensities or powers - not just in military and commercial sonar, but in acoustics generally, and in electrical engineering such as amplifier design.
The Richter Scale and the magnitude scale of star brightness are logarithmic. Common and hyperbolic logarithms crop up in many places - the latter control the expansion or compression of gas in an engine or compressor cylinder, for example.
Exponents also facilitate handling very large & very small numbers by turning them into multiples of plus or minus powers of 10.
What is the slope x 4y equals 12?
I presume that since you labeled this as a Calculus problem that you mean x * 4y = 12?
x * 4y = 12 --->
4y = 12 / x --->
y = 3 / x --->
y = 3 * x^(-1)
You will notice that this function is not a line, but a curve. The slope will be different at different points on the line. Thus, we can't find the slope of the entire function, but we CAN find a function which gives us the slope of a tangent line at any point on the function. We do this by taking the derivative.
For f(x) = a * x^(n)
f'(x) = a * n * x^(n-1)
Using a = 3 and n = -1, we have:
y = f(x) = 3 * x^(-1)
dy/dx = f'(x) = 3 * -1 * x^(-1 - 1) = -3 * x^(-2)
So your answer will be:
dy/dx = -3 * x^(-2)
What does x plus 1 mean in relation to functions?
If the question is what I think it is, then it means a translation of the graph by 1 unit to the left.
What are limits and why you use them?
Limits give upper and lower bounds for integration. One simple example is in finding an enclosed area. The upper and lower limits form vertical lines which enclose an area between the function and the x-axis and then integration from the lower limit (smaller x boundary) to the upper limit (larger x boundary).
Is y equals x differentiable at origin?
Yes, but only if the domain is the real numbers. The derivative is y = 1.
Why in dissolution S1 stage limit is Q plus 5 percent and in S2 stage is Q percent?
because dissolution involves the changing of substances from q plus 5 but when s2 stage is present q is removed
-2x squared plus x plus 1 divided by x-1?
(-2x2 + x + 1) / (x - 1)
= (-2x - 1)(x - 1)/(x - 1)
= -2x - 1
How do you solve 3x plus seventeen?
set the equation equal to zero: 3x + 17=0
subtract 17 from both sides so you end up with : 3x=-17
divide both sides by 3 to isolate x: x=-17/3
your answer is -17/3
Who remembered the most digits for pi?
By memory, it is Hiroyuki Goto, who memorized and recited 42,195 in seventeen hours and twenty one minutes in 1995.
What is a special relation that pairs each x-value with exactly one y-value?
It is called a function.
What type of lines of lines are these y equals 2x and 2y-x plus 4?
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. The second line is, in fact not a line because all you have is an expression, not a equation.
Depending on where the equality sign appears, the two lines could intersect at right angles of not.
Is 3y plus 2 equals 0 a linear function?
It is not a linear function because it is missing x as the input variable
