Ch 1 Maths Class 12 Notes
Handwritten notes of Ch 1 Maths Class 12 Notes written by Professor Rana Azhar. These notes are very helpful in the preparation of the ch 1 math class 12 for the students of Mathematics of the intermediate and these are according to the paper patterns of all Punjab boards.
Summary and Contents:
Topics which are discussed in the notes are given below:
- Important ch 1 maths class 12 important questions for Intermediate part-II students.
- Historically, the term function was first used by German mathematician Leibnitz (1646-1716) in 1673 to denote the dependence of one quantity on another e.g.
- 1) The area "A" of a square of side "x" is given by the formula A=x². As area depends on its side x, so we say that A is a function of x.
- 2) The area "A" of a circular disc of radius "r" is given by the formula A=πr² As area depends on its radius r, so we say that A is a function ofr.
- 3) The volume "V" of a sphere of radius "r" is given by the formula 4 V=-π³ 3 3 3 As volume V of a sphere depends on its radius r, so we say that V is a function of r.
- The Swiss mathematician, Leonard Euler conceived the idea of denoting function written as y=f(x) and read as y is equal to f of x. f(x) is called the value of f at x or image of x under f.
- The variable x is called independent variable and the variable y is called dependent variable off. If x and y are real numbers then fis called real valued function of real numbers.
- Important class 12 maths ncert solutions ch 1 ex 1.1 for Intermediate part-II students.
- Domain of the function: If the independent variable of a function is restricted to lie in some set, then this set is called the domain of the function e.g. Dom off = {0≤x≤5)
- Range of the function: The set of all possible values of f(x) as x varies over the domain of f is called the range of fe.g. y = 100-4x². As x varies over the domain [0,5] the values of y = 100-4x² vary between y=0 (when x=5) and y=100 (when x=0) Range of f= {0≤ y ≤ 100}
- Important class 12 maths ch 1 ex 1.1 for Intermediate part-II students.
- Definition:A function is a rule by which we relate two sets A and B (say) in such a way that each element of A is assigned with one and only one element of B. For example is a function from A to B its Domain = {1,2,3} and Range = {4,5}
- Important ch 1 maths class 12 pdf for Intermediate part-II students.
- Definition of Even function with example
- Definition of Odd function with example
- Definition of continuity and its conditions
- State and Prove sandwich theorem
- Find the domain and range of a function
- In general: A function f from a set 'X' to a set 'Y' is a rule that assigns to each element x in X one and only one element y in Y. (a unique element y in Y). If an element "y" of Y is associated with an element "x" of X, then wer write y=f(x) & read as "y" is equal to f of x. Here f(x) is called image of f at x or value of f at x.
- Examples, Theorems, and Exercise problems with their solutions.
- Important ch 1 maths class 12 ex 1.1 for Intermediate part-II students.
- Important ch 1 maths class 12 ex 1.2 for Intermediate part-II students.
- Important ch 1 maths class 12 ex 1.3 for Intermediate part-II students.
- Important class 12 math ch 1 ex 1.4 for Intermediate part-II students.