Class 12 Math Chapter 1 Solutions
Handwritten notes on Class 12 Math Chapter 1 Solutions written by Professor Sulman Sherazi Suib. These notes are very helpful in the preparation of the Class 12 Math Chapter 1 Solutions of the Functions and Limits 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 Multiple Choice Questions class 12th maths chapter 1 mcqs Limits and Continuity of 2nd Year Mathematics
- Important Theorems with their Applications of Chapter No. 1: Limits and Continuity of 2nd Year Mathematics
- Important 12th class math chapter 1 exercise 1.1 for Intermediate part-II students.
- Important Continuity and discontinuity of a function in Graphical representation of Chapter No. 1: Limits and Continuity of 2nd Year Mathematics State and Prove Sandwich Theorem of Chapter No. 1: Limits and Continuity of 2nd Year Mathematics Function:- A function from a set X to a set Y is a rule or correspondence that assigns to each element xin X a unique element y in Y. The set X is called domain off. The set of corresponding elements y in Y is called range of f If a variable y depends on a variable x in such a way that the value of x determines exactly one value of y, then we say that "y is function of x".
- Important 12th maths exercise 1.1 answers pdf for Intermediate part-II students.
- SWISS mathematician EULER (1707-1783) invented a symbolic way to write a statement "y is a function of x" as y=f(x) which is read as "y is equal to fof x".
- Important 12th maths exercise 1.1 solutions for Intermediate part-II students.
- NOTE:- The term function was recognized by GERMAN mathematician LEBNITZ (1646-1716). Domain: The set of all possible inputs of a function is called domain. *The domain of every function f(x) is set of all real numbers for which f(x) is defined. The values at which f(x) becomes undefined or complex valued will be excluded from real numbers. Domain is also known as pre-images.
- Important exercise 1.1 class 12 maths pdf download for Intermediate part-II students.
- Range: The set of all possible out puts of a function is called range. Range is also known as images.
- Definition of Even function with example
- Definition of Odd function with example
- Important exercise 1.1 class 12 maths solutions for Intermediate part-II students.
- Definition of continuity and its conditions
- State and Prove sandwich theorem
- Find the domain and range of a function
- Important 12th class math exercise 1.1 for Intermediate part-II students.
- Important 12th math 1.1 solution for Intermediate part-II students.
- Important 1.1 exercise class 12 for Intermediate part-II students.
- Important exercise 1.1 class 12 for Intermediate part-II students.
- Important ex 1.1 class 12 maths for Intermediate part-II students.
- Important ex 1.1 class 12 ncert solutions for Intermediate part-II students.
- Polynomial Function: A function P of the form P(x) = anx^n+an-1x^n-1+-----an for all x, where the cofficients an, an-1..... a2, a1,an are real numbers and the exponents are non-negative function.
- Linear Function: If the degree of polynomial function is 1, then it is called linear function.
- Quadratic function: If the degree of polynomial function is 2, then it is called a quadratic function.
- Identity Function: A function for f(x) = x or y = x is called identity function. It is denoted by I.
- Constant Funtion: A function for which f(x) = b or y=b is called constant function.
- Rational Function: The quotient of two polynomials such as f(x) = p(x) / Q(x) where Q(x) is not equal to zero is called rational function.
- Exponential Function: A function in which the variable appears as exponent (power) is called exponential function. e.g y=e^ax etc.