Calculas (A branch of Maths)

Calculas (a branch of Maths)

     It is a mathematics of change. Calculas was invented in the 17th century by Isaac Newton of U.K. and Gottfried Wilhelm Leibniz of Germany. Newton applied the calculas to formulate his laws of motion and gravitation.

1)  Limits :

      lim x—>a  f(x)    ( Where x—>a " x tends to "a")

      Difference "D" :

       (x—>a) : Means that (x) gets nearer and nearer to (D).

       (x=0) : Means that (x) takes the value (D).

E.g. lim x–>2   x²- 4/ (x-2)
    = lim x–>2  (x+2)(x-2)/(x-2)
    = lim x–>2  (x+2)     (bcuz (x-2) is concelled )
    = 2+2 = 4

2) Properties of limits :
     Let (f) and (g) be two functions of x then,

• For any constant C

      lim x–>a  C  =  C

• lim x–>a [f(x)+g(x)] = lim x–>a  f(x) + lim x–>a  g(x)
• lim x–>a [f(x)- g(x)] = lim x–>a  f(x) - lim x–>a  g(x)
• lim x–>a [k f(x)] = k lim x–>a f(x)  where "k" is any Real Number.
• lim x–>a [f(x).g(x)] = [lim x–>a f(x)][lim x–>a g(x)]
• lim x–>a [f(x)/g(x)] = [lim x–>a f(x)]/ [lim x–>a g(x)]     Provided lim x–>a  g(x) ≠ 0

•