Preparation for Calculus Function

Calculus (Latin, calculus, a small stone used for counting) is a branch in mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. In this article we hall discuss about preparation for calculus function.(Source: Wikipedia).


Preparation for operations of functions

A function exactly has four basic operations of algebra (addition, subtraction, multiplication, and division). Functions are combined by these fundamental operations; the domain of the new combined function is only the elements that were shared by the domains of the original functions.

Preparation of some formula for combining functions:

• The sum of two function f and function g: (f + g)(x) = f(x) + g(x) .

• The difference of two functions, f and function g: (f - g)(x) = f(x) - g(x) .

• The product of two functions, f and function g: (fg)(x) = f (x)×g(x) .

• The quotient of two functions f and g: (f/g) (x) = f(x)/g(x). If g(x) = 0

Preparation for calculus functions with example

Example 1:

The gradient at any point (x , y) of a curve is 3x2-12 and the curve passing point(, -7), find the equation of the curve.

Solve  `(dy)/(dx)` =3x2-12

Integration both sides, we get  y= `int` (3x2-12)dx or y=3 X `(x^3)/(3)` -12 + c.

Where c is a constant of integration. Or y=x3-12x+c

If you have problem on these topics Alternate Interior Angle Definition .

C can be found from the consideration that this equation is satisfied by the values x=2 and y=-7.

Therefore -7=8-24+c

Therefore c=9

Substituting in equation we get y=x3-12x+9m which is the required equation of the curve.