Fsc Part 2 Math Notes. Exercise 1.3 (Solution) Mathematics 2nd Year. By Khurram Farooq Last updated Sep 13, 2018. Share Facebook Twitter Google+ ReddIt WhatsApp.

FSc Part 2 (2nd Year) Math Notes/Solutions There are seven chapters of 12th class math.we have work hard to make them easy and suitable solution for students and teachers۔ Here we will present the chapter wise notes of whole. 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. In this online lecture,Muhammad Naveed Jaffar explains FSC part 2 Mathematics Chapter 1 Functions and Limits.The topic being discussed is Topic Exercise 1.1. Fsc Part 2 Math Notes. Exercise 2.5 (Solution) Mathematics 2nd Year. By Khurram Farooq Last updated Sep 13, 2018. Share Facebook Twitter Google+ ReddIt WhatsApp.

Notes (Solutions) of Unit 02: Differentiation, 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.

Here are few online resource, which are very helpful to find derivative. Macos catalina download 10.15.

Contents & summary

• • Average Rate of Change
• Finding $f'(x)$ from Definition of Derivative
  • Exercise 2.1
• • Exercise 2.2
• • Exercise 2.3
• Derivatives of Inverse Function
• Derivative of a Function given in form of parametric Equations
• • Exercise 2.4
• Derivatives of Inverse Trigonometric Functions
• Derivative of Exponential Functions
• Logarithmic Differentiation
• Derivative of the Inverse Hyperbolic Function
• Successive Differentiation ( or Derivatives)
• Series Expansions of Function
• • Exercise 2.8
• Increasing and Decreasing Function
• Critical Values and Critical Points
  • Exercise 2.10

Which method is better

In this chapter many questions can be solved in much easier way. Actually in every exercise some formula/method is introduced to solve the question. In examination it is not necessary to do the same method as given in exercise. Here is one example:

We have to find the derivative of $frac{x+1}{x-1}$ with respect to $x$. Rockstar editor pc download.

Method 1

$$begin{aligned}frac{d}{dx}left(frac{x+1}{x-1}right) &= frac{(x-1)frac{d}{dx}(x+1)-(x+1)frac{d}{dx}(x-1)}{(x-1)^2}&= frac{(x-1)(1)-(x+1)(1)}{(x-1)^2}&= frac{x-1-x-1}{(x-1)^2}&= frac{-2}{(x-1)^2}end{aligned}$$

Method 2

By converting improper to proper fraction $$frac{x+1}{x-1}= 1+frac{2}{x-1}=1+2(x-1)^{-1}$$Now$$begin{aligned}frac{d}{dx}left(frac{x+1}{x-1}right) &=frac{d}{dx}left(1+2(x-1)^{-1}right)&= 0-2(x-1)^{-2}(1)&= frac{-2}{(x-1)^2}end{aligned}$$ Avr loader v1.0 beta.

This was a simple example but try it to find the derivative of $frac{x^2+1}{x^2-1}$.

Solutions

• Exercise 2.1 | View Online | Download PDF (156KB)

• Exercise 2.2 | View Online | Download PDF (130KB)

• Exercise 2.3 | View Online | Download PDF (209KB)

• Exercise 2.4 | View Online | Download PDF (175KB)

• Exercise 2.5 | View Online | Download PDF (239KB)

• Exercise 2.6 | View Online | Download PDF (236KB)

• Exercise 2.7 | View Online | Download PDF (194KB)

• Exercise 2.8 | View Online | Download PDF (147KB)

• Exercise 2.9 | View Online | Download PDF (200KB)

• Exercise 2.10 | View Online | Download PDF (180KB)

Math Notes 2nd Year Fsc 2.1

The following notes was written and sent by Mr. Amir Shehzad.

• Unit 02: Differentiation | Download PDF (1.53 MB)

Here are previous and next chapters

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 Intermediate and Secondary Education (FBISE), Faisalabad Board, Multan Board, Sargodha Board, DG Khan Board, Gujranwala Board, Rawalpindi Board or others board of Punjab, Pakistan. These 12 Class Math Notes are obtained from mathcity.org.

Math Notes 2nd Year Fsc 1.3

You Can Easily View or Download These Notes For PC. To view PDF files, there must be PDF Reader (Viewer) installed on your computer. Click Here to Download PDF Viewer and other Softwares.

Chapter # 1 Functions and Limits

Chapter # 2 Differentiation

Chapter # 3 Integration

Chapter # 4 Introduction to Analytic Geometry

Chapter # 5 Linear Inequalities and Linear Programming

Math Notes Fsc Part 2

Chapter # 6 Conic Section

Chapter # 7 Vectors