MATH-M 211 Lecture Notes - Lecture 1: Trigonometric Functions
Document Summary
Approaching idea will be called a limit, and slope of tan line will be the derivative: slope = y2 y1 = y x2 x1 x. X is considered 1 variable: ( x)2 = x2 delta ( ) represents change ( x 0) Slope of tan line changes at each different point of a function. Equation of a tangent line: use point-slope form or slope-intercept form. Slope-intercept y y1 = m(x x1) y = mx + b. Find mtan for y = x2 at any point (x, y) Rewrite first point on secant line as (x, y) as (x, x2) Rewrite second point as (x + x, (x + x)2) msec = (x + x) 2 x + x x: denominator must always reduce to x msec = x 2 + 2x x + x. 2: all terms without x must cancel in numerator. X msec = 2x + x: must always have written conclusion.
