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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

Find the x-intercept of the equation x plus 2y equals 8?

x+2y=8

The x-intercept is the value of x when y=0, therefore substitute y=0 into the equation:

x+0=8

therefore, x=8

The coordinates of this point is (8,0)

Does a trapezoid's opposite sides parallel?

One pair must be. If the other pair is also parallel it becomes a parallelogram.

How would you differentiate -3cosy times x squared?

((-3)cos(y))(x2)

Well first of all you need decide what rule you should use. Now, because they're multiplied together I'm going to use the product rule which is -

(dy/dx)= f'g +fg'

remember to write everything out -

f=((-3)cos(y))

f'=((3)sin(y))

g=x2

g'=2x

so from here it's pretty simple, you just sub in the values you have for each letter, remember to use brackets!

so....(dy/dx)= ((3)sin(y))(x2)+((-3cos(y))(2x)

Now you just need to simplify and gather like terms -

(dy/dx)=3x2siny-6xcosy

=3x(xsiny-cosy)

And there you have it!

Remember to check this yourself cause its been a while since I've studied this so I might have made a silly mistake somewhere. ^_^ Hope this helps!

Common multiples of 2 and 3?

6 12 18 24, etc. if you need both, 2, 4, 6 8 10, or 3, 6, 9, 12, if you need only one.

Why it takes several seconds for the odor of ammonia to travel a few feet?

Because the NH3 molecules have to travel through the nitrogen and oxygen molecules in the atmosphere.

What is the area of a 2 x 4?

It depends on the length. The surface area would be 4*length+8*length+16.

How is Infinite used in real life applications?

There is really nothing infinite in real life. But there are several cases where for practical purposes, "infinity" is almost the same as "very large". One example is in optics, where it is not so much the distance from the lens to the object that matters, but the RECIPROCAL of the distance. In this distance, since the reciprocal of a very large number is close to zero, a far-away object (e.g., the Sun) can be approximated as "infinitely far away".

What is 4x y-3xy plus 15xy-12 plus 9xy -14xy plus 19 plus -13x y plus 7xy plus 16xy plus 21?

It is not clear whether the spaces that appear between some xy pairs are intentional or whether they should have had some other symbols.

Ignoring those spaces, 21xy + 28.