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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 answer to x - 3 equals 4?

x= 7

You have x-3= 4

Add 3 to both sides to cancel out the -3

This leaves you with x=7

How do you find the extreme values of x2lnx?

Taking the derivative:

2lnx+2, 2(lnx+1).

Extrema occur at y'=0.

2(lnx+1)=0,lnx=-1

x=e^(-1)=1/e

y=-2/e

So the extrema occurs at (1/e,-2/e)

How many Kl equal to milliliter?

1 liter = 1000 ml

1000 liters = 1 Kilolitre

1 Kiloliters = 1000 litres = 1000 x 1000 ml = 2000 ml

Thus, 1 Kl is 1 million (1000000) milliliters.

What do you call the width of the index finger?

There is no scientific name for the width of the index finger. The name index finger literally means pointing finger.

Does y equals 2 x plus 3 mean 3 units up?

In a sence it does; it means 3 units up on the y-axis, which is the point at which it crosses the y-axis.

Why is there one million cubic centimeter in a cubic meter?

Because we muliply the three sides of a cube of one meter length x 3. =1000x1000x1000=1,000,000

How do you test to see if a graph is a function?

The test is: If you were to draw a vertical line through every point in the domain (every x-value that is allowed), would it intersect the graph in exactly one point? Rather than draw lines, you could just slide a ruler, keeping it parallel to the vertical (y) axis.

If no intersection, then it is not a function because there is a point in the domain which has no image in the range.

If more than one intersection, then it is not a function because there is a point in the domain that is mapped to more than one value in the range.

What is the derivative and second derivative of lnx to the third power?

If you mean: y =(lnx)3

then:

dy/dx = [3(lnx)2]/x

ddy/dx = [(6lnx / x) - 3(lnx)2] / x2

If you mean: y = ln(x3)

Then:

dy/dx = 3x2/x3 = 3/x = 3x-1

ddy/dx = -3x-2 = -3/x2