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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

16x2 plus 8x plus 1 equals 0?

16x2 + 8x + 1 = 0 : This factorises to (4x + 1)(4x + 1) = 0

When 4x + 1 = 0 then 4x = -1 : x = -1/4.

What is 3x plus 2 equals 2x plus 8?

3x+2=2x+8
x=6

3x+2 = 2x + 8; first subtract 2x from both sides
x+2=8; then subtract 2 from both sides
x=6

What is x squared minus 4 divided by 4x plus 12?

(x2 - 4)/4x = 12; x ≠ 0

x2 - 4 = 48x

x2 - 48x = 4

x2 - 48x + 242= 4 + 242

(x - 24)2 = 4 + 576

x - 24 = ±√580

x = 24 ± 2√145

Is the function y x - 5 a straight line?

Probably yes. Unfortunately, though, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to be certain.

How do you graph x plus y equals -5?

Put x = 0. The equation is then y = 0 + 5 or y = 5

Mark the point (0,5).

Put y = 0. The equation then becomes 0 = x + 5 or x = -5

Mark the point (-5, 0)

Joint the two points and extend the line in both directions.

How do you prove in 3 different ways that the line of y equals x -4 is tangent to the curve of x squared plus y squared equals 8?

If: y = x-4 and y = x2+y2 = 8 then 2x2-8x+8 = 0 and the 3 ways of proof are:

1 Plot the given values on a graph and the line will touch the curve at one point

2 The discriminant of b2-4ac of 2x2-8x+8 must equal 0

3 Solving the equation gives x = 2 or x = 2 meaning the line is tangent to the curve

What is an example of using recursive functions?

Let's take the example of finding the factorial of a number (of a positive integer). The factorial of N is N * (N-1) * (N-2) * (N-3) ... * 3 * 2 *1 It is the product of all integers between that number (including that number) and 1. For example, factorial 2 = 2*1 = 2 factorial 3 = 3*2*1 = 6 factorial 4 = 4*3*2*1= 24 Now you define a recursive function Fac (N) as Fac (N) = Fac (N-1) * N, with Fac(1) predefined as 1. Thus, Fac(N-1) = Fac(N-2) * (N-1) and Fac(N-2) = Fac(N-3) * (N-2) and thus recursion takes over until such time fac(1) needs to be evaluated. We know the value of Fac(1) which is set as 1. Thus we can evaluate Factorial(N) using recursion.

How do you find the x intercept for x2 36 plus y2 64 equals 1?

It seems that it is the equation of an ellipse, x2/b2 + y2/a2 = 1, with center at the origin, a vertical major axis with length 2a, and a horizontal minor axis with length 2b.

x2/36 + y2/64 = 1

Since you are looking for the x-intercepts, they are (√b2, 0) = (√36, 0) = (6, 0) and (-√b2, 0) = (-√36, 0) = (-6, 0)

Graph the equation y equals 2x plus 1?

So, if we see the basic equation y=mx+b, we see that m=2, and b=1.

If you look closely, this is basic rotation and translation of the original graph.

First, I would translate the "mother graph" (y=mx) and then translate one up.

Then, we would rotate the graph to the right two units.

When did William Hyde Wallostan discover palladium?

William Hyde Wollaston discovered palladium in 1803. Wollaston, a physicist and chemist, was born in East Dereham, Norfolk, England on August 6, 1766.