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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 range of the equation y equals x2 plus 4?

This equation describes a parabola, so it's range on the x-axis will be infinite. To find it's vertex, we can take it's derivative and solve for zero:

y = x2 + 4

y' = 2x

Let y' = 0

0 = 2x

x = 0

Now we plug that x value into the original equation to find y:

y = 02 + 4

y = 4

So the vertex is at the point (0, 4). To see whether that's a minimum or a maximum, we need only take it's second derivative and check whether it's positive or negative at that point:

y' = 2x

y'' = 2

So the rate of change of the slope is positive, which means that the parabola's vertex is a minimum. We can say then that the equation has an infinite x range, and a y range from 4 to infinity.

Examples of constant speed but changing acceleration?

A body moving with constant speed in a circular path has acceleration changing at every point.

6x2 - 4x plus 25 is a trinomial?

Yes, 6x2 - 4x + 25 is a trinomial. This is because there are three terms (thus the name trinomial), which are "connected" by operations of addition and subtraction: 6x2, 4x, and 25.

If you mean to ask how to factor this particular trinomial, please specify so in your question.

What is stochastic testing?

Stochastic testing is the same as "monkey testing", but stochastic testing is a lot more technical sounding name for the same testing process.

Stochastic testing is black box testing, random testing, performed by automated testing tools. Stochastic testing is a series of random tests over time. The software under test typically passes the individual tests, but our goal is to see if it can pass a large number of individual tests.

Find the length of 8 plus 7x?

Without knowing the value of x and the required unit of length then a meaningful answer to this question cannot be provided.

What is the answer of 2x-4 over x squared minus 4?

First, factorise both numerator and denominator:

(2x - 4) / (x2 - 4)

= 2(x - 2) / (x + 2)(x - 2)

= 2 / (x + 2).

Do all functions of the form yax2 have the same vertex and axis of symmetry?

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. Please resubmit your question spelling out the symbols as "plus", "minus", "equals", "squared".

I suspect the answer is yes, but it all depends on the exact form of the equation.

What do you know about a function that is made up of ordered pairs in such a way that the same y-value appears in a correspondence with two different x-values?

For example, y = ax2 + bx + c (the equation of a parabola).

Every parabola has an axis of symmetry and the graph to either side of the axis of symmetry is a mirror image of the other side. It means that if we know a point on one side of the parabola, we can find its symmetric point to the other side, based on the axis of symmetry. Those symmetric points have opposite x-coordinate values, and the same y-coordinate value. The vertex only is a single point which lies on the axis of symmetry.

What is the effect of latitude on acceleration due to gravity?

The equation for the force of gravity is F=-GMm/r2 at the equator the earth has more mass due to the gravity of the sun distroting the sherical shape of the earth. But this mean that the distance between the centre of the earth to the poles (r) is less and because r is squared the effect of distance has more of an impact than the mass so this means that gravity is stronger at the poles and weaker at the equator.....

What has the US done for the world?

# The first democratic nation # Separation of Church & State # Habeas Corpus # Bill of Rights # Federal Constitution # Checks & Balances # Free press # Meritocratic society # Decisive interventions in WWI and WWII # Facilitated decline of Soviet Union

What is 2y plus 3 when y equals 3?

Simply substitute a 3 in for y. 2(3) + 3 = 6 + 3 = 9.

Note: If this question is from work you have been assigned by a teacher or professor, I suggest you do the work yourself instead of trying to find the answers online. This will help you to better understand the material and become more familiar with it. Of course, if this question was not from homework, you can ignore this message.

What is the answer to x plus y to 3rd power plus x minus y to 3rd power?

(x + y)3 + (x - y)3 = (x3 + 3x2y + 3xy2 + y3) + (x3 - 3x2y + 3xy2 - y3)

= 2x3 + 6xy2 = 2x*(x2 + 3y2)