1. We will start from Chapter 2 Sections 2.1 to 2.8 MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag

2. Chapter 2 : Limits and Derivatives The idea of a limit is illustrated by secant lines approaching a tangent line. The Book Says: MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag

3. Slope and Equation of a line MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag How to find the slop of a line? (x 1, y 1 ) (x 2, y 2 ) How to find the equation of a line?

4. Secant line and Tangent line MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag What is the difference ?? The word tangent is derived from the Latin word tangens, which means “touching.” Tangent line

5. Secant line and Tangent line MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag How to find the slope of these lines ?? Tangent line

6. Secant line and Tangent line MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag

7. Secant line and Tangent line MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag

8. Secant line and Tangent line MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag

9. Secant line and Tangent line MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag

10. 2.1 THE TANGENT PROBLEM The Book Says: MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag 1 1 1 1.5 2.25 Q tangent line

11. 2.1 THE TANGENT PROBLEM The Book Says: MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag 1 1 1 1.5 2.25 Q tangent line 1.2 2.51.5 2.21.2 ---

12. 2.1 THE TANGENT PROBLEM The Book Says: MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag 1 1 1 x X^2

13. 2.1 THE TANGENT PROBLEM MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag 23 1.52.5 1.1 2.1 1.012.01 1.0012.001 1.02.0 tangent line secant line Slope of the tangent line = 2.0

14. 2.1 THE TANGENT PROBLEM MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag 10 1.50.5 1.90.9 1.990.99 1.9990.999 1.02.0 tangent line secant line Equation of the tangent line

15. 2.1 THE TANGENT PROBLEM MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag 10 1.50.5 1.90.9 1.990.99 1.9990.999 1.02.0 tangent line secant line

16. 2.1 THE TANGENT PROBLEM MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag