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

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Presentation transcript:

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

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

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

2.1 THE TANGENT PROBLEM MATH 101 : CALCULUS I – Dr. Faisal Fairag tangent line secant line Slope of the tangent line = 2.0

2.1 THE TANGENT PROBLEM MATH 101 : CALCULUS I – Dr. Faisal Fairag tangent line secant line Equation of the tangent line Slope = 2.0 point = (1, 1)

2.1 THE TANGENT PROBLEM MATH 101 : CALCULUS I – Dr. Faisal Fairag tangent line secant line

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