- Very helpful notes for the students of 2nd year to prepare their paper of Maths according to syllabus given by Federal Board of Intermediate and Secondary Education (FBISE), Faisalabad Board, Multan Board, Sargodha Board, DG Khan Board, Gujranwala Board, Rawalpindi Board or others board of Punjab, Pakistan.
- FSc Part 1 Mathematics Notes/Solutions FSc Part1 PTB Book Cover Notes (Solutions) of Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB) Lahore. There are fourteen chapters in this book and we have work hard to make easy and suitable solution for students and teachers so that it help them learn things quickly and easily.
- FSc second year Biology, Chemistry, Math, Physics, English, Urdu, Pakistan Studies, Computer and all other subjects’ notes are available here. As you know, at FSc level, there are two field of study; FSc Pre Engineering & FSc Pre medical.
Jan 12, 2020 Mathematics 2nd Year All Chapter Notes Math FSc Part 2 “Class 12 Mathematics Notes” Mathematics-XII (Punjab Text Book Board, Lahore) These Mathematics-XII FSc Part 2 (2nd year) Notes are according to “Punjab Text Book Board, Lahore”. Very helpful notes for the students of 2nd year to prepare their paper of Maths according to syllabus given by Federal Board of. Jan 12, 2020 Also you will find answers of all exercises questions, solved examples, paper schemes, model papers and old papers solution of Federal Board (FBISE), Lahore board, Sialkot Board, Rawalpindi Board and other boards of Punjab, Pakistan. Download 1st year and 2nd year mathematics notes for free. Please select your class from below.
Notes (Solutions) of Unit 01:Functions and Limits, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Software section.
Contents & summary
- Concept of Function
- Notation and Values of a Function
- Graph of Functions Defined Piece-Wise
- Algebraic Function
- Inverse Trigonometric Functions
- Exponential Function
- Hyperbolic Function
- Explicit Function
- Odd Function
- Composition of Function and Inverse of a Function
- Inverse of a Function
- Exercise 1.2
- Meaning of the phrase “x approaches Zero”
- Concept of Limit of a Function
- Theorems on Limits of Function
- $lim_{xto a}frac{x^n-a^n}{x-a} = na^{n-1}$, where n is an integer and a>0
- $lim_{xto0}frac{sqrt{x+a} - sqrt{a}}{x} = frac{1}{2sqrt{a}}$
- Methods for Evaluating the limits at Infinity
- $lim_{xto0}frac{a^x-1}{x} = {log_e}^a$
- If $theta$ is measured in radian, then $lim_{thetato 0}frac{sintheta}{theta} = 1$
- Continuous and Discontinuous Function
- Criterion for Existence of Limit of a Function
- Exercise 1.4
- Graph of the Exponential Function $f(x) = a^x$
- Graph of Common Logarithmic Function $f(x) = log x$
- Graph of natural logarithmic Function $f(x) = ln x$
- Graph of parametric Equations
- Graphical Solution of the Equations
Consider two functions $f(x)=x+3$ and $displaystyle g(x)=frac{x^2-9}{x-3}$. Is $f=g$? (see answer here)
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- Exercise 1.2 | View online | Download PDF
Math Notes 2nd Year Fsc 1.5
- Exercise 1.4 | View online | Download PDF
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2nd Year Chemistry Notes
- Unit 01: Function & Limits (Complete notes with MCQs) | Download PDF (0.7 MB)