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

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)

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

Sec 2.1: The Tangent Problem (Example 1)

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

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

Sec 2.1: The Tangent Problem (Example 1)

Sec 2.1: The Tangent Problem (Example 1)