1. Chapter 2 Sec. Topics 2.1 The Tangent Problem (Example 1). 2.2
The Limit of a Function.
2.3
Calculating Limits Using the Limit Laws 
2.4
The Precise Definition of a Limit (Examples 1,2 and 3)
2.5
Continuity
2.6
Limits at Infinity; Horizontal Asymptotes 
2.7
Derivative and Rates of Change
2.8
The Derivative as a Function + Exercise # 56

2. Sec 2.1: The Tangent Problem (Example 1)
Slope and Equation of a line
How to find the slop of a line?
How to find the equation of a line?
(x1, y1)
(x2, y2)

3. Sec 2.1: The Tangent Problem (Example 1)
Tangent line
Secant line
What is the difference ?? Lines??
a line joining two points of
a curve is a secant to the curve.
The word tangent is derived from the Latin word tangens, which means “touching.”
slope of a curve at a point P on the curve?
the slope of the tangent at P.

4. Sec 2.1: The Tangent Problem (Example 1)
Is it possible that a line could be tangent and secant in the same time

5. Sec 2.1: The Tangent Problem (Example 1)
Secant line and Tangent line
Tangent line
How to find the slope of these lines ??

6. Sec 2.1: The Tangent Problem (Example 1)
Secant line and Tangent line

7. Sec 2.1: The Tangent Problem (Example 1)
Secant line and Tangent line

8. Sec 2.1: The Tangent Problem (Example 1)
Secant line and Tangent line

9. Sec 2.1: The Tangent Problem (Example 1)
Secant line and Tangent line

10. Sec 2.1: The Tangent Problem (Example 1)
Secant line and Tangent line

11. Example : Sec 2.1: The Tangent Problem (Example 1)
Find the slope of the tangent line to the prabola at the point
tangent line
2.25 Q
1.44 1 1
1.2
1.25

12. Example : Sec 2.1: The Tangent Problem (Example 1)
Find the slope of the tangent line to the prabola at the point
tangent line
2.25 Q
1.44 1 1
1.2
1.25

13. Example : Sec 2.1: The Tangent Problem (Example 1)
Find the slope of the tangent line to the prabola at the point
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

14. Example : Sec 2.1: The Tangent Problem (Example 1)
Find the slope of the tangent line to the prabola at the point
X^2 1 1 x

15. Slope of the tangent line = 2.0
Sec 2.1: The Tangent Problem (Example 1)
secant line 2 3
1.5
2.5
2.1
1.1
1.01
2.01
1.001
2.001
1.0
2.0
tangent line
Slope of the tangent line = 2.0

16. Sec 2.1: The Tangent Problem (Example 1)
means as

17. Equation of the tangent line
Sec 2.1: The Tangent Problem (Example 1)
Example :
Find the equation of the tangent line to the prabola at the point
Equation of the tangent line
Slope = 2.0
point = (1, 1)

18. Sec 2.1: The Tangent Problem (Example 1)

19. Sec 2.1: The Tangent Problem (Example 1)
How to find a slope of a tangent line to the curve f (x) at the point (a, b) h as

20. Sec 2.1: The Tangent Problem (Example 1)
EXAM-1 TERM-081
EXAM-1 TERM-141
EXAM-1 TERM-132

21. Sec 2.1: The Tangent Problem (Example 1)

22. Sec 2.1: The Tangent Problem (Example 1)