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

3. Slope and Equation of a line MATH 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. MATH 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 Secant line

5. Is it possible that a line could be tangent and secant in the same time

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

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

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

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

10. Secant line and Tangent line MATH 101 : CALCULUS I – Dr. Faisal Fairag

11. Secant line and Tangent line MATH 101 : CALCULUS I – Dr. Faisal Fairag

12. 2.1 THE TANGENT PROBLEM The Book Says: MATH 101 : CALCULUS I – Dr. Faisal Fairag 1 1 1 1.5 2.25 Q tangent line

13. 2.1 THE TANGENT PROBLEM The Book Says: MATH 101 : CALCULUS I – Dr. Faisal Fairag 1 1 1 tangent line

14. 2.1 THE TANGENT PROBLEM The Book Says: MATH 101 : CALCULUS I – Dr. Faisal Fairag 1 1 1 1.2 1.44 Q tangent line

15. 2.1 THE TANGENT PROBLEM The Book Says: MATH 101 : CALCULUS I – Dr. Faisal Fairag 1 1.5(1.5,2.25)2.5 1.2(1.2,1.44)2.2 1.1(1.2,1.21)2.1 1.01(1.01,1.0201)2.01

16. 2.1 THE TANGENT PROBLEM The Book Says: MATH 101 : CALCULUS I – Dr. Faisal Fairag 1 1 1 x X^2

17. 2.1 THE TANGENT PROBLEM MATH 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

18. 2.1 THE TANGENT PROBLEM MATH 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 Slope = 2.0 point = (1, 1)

19. 2.1 THE TANGENT PROBLEM MATH 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

20. 2.1 THE TANGENT PROBLEM MATH 101 : CALCULUS I – Dr. Faisal Fairag

23. 0.33330.5 0.26320.9 0.25130.99 0.25010.999 0.21.5 0.23811.1 0.24881.01 0.24991.001