MTH101 Formula Sheet

MTH101: Calculus and Analytical Geometry

Midterm Formula Sheet (Lessons 1 - 22)

1. Coordinates and Lines (Lessons 1-4) · Slope (m): m = (y2 - y1) / (x2 - x1) · Slope-Intercept Form: y = mx + b · Point-Slope Form: y - y1 = m(x - x1) · General Equation: Ax + By + C = 0 · Parallel Lines: m1 = m2 · Perpendicular Lines: m1 × m2 = -1 · 2. Distance and Circles (Lesson 5) · Distance Formula: d = √[(x2 - x1)2 + (y2 - y1)2] · Midpoint Formula: M = ((x1+x2)/2 , (y1+y2)/2) · Standard Circle Equation: (x - h)2 + (y - k)2 = r2 · 3. Limits and Continuity (Lessons 9-13)

Special Trig Limit: limx→0 (sin x / x) = 1 Continuity Condition: limx→c f(x) = f(c)

4. Differentiation Rules (Lessons 15-20) · Rule Name · Formula

Power Rule

d/dx(xn) = nxn-1

Product Rule

(fg)' = f'g + fg'

Quotient Rule

(f/g)' = (f'g - fg') / g2

Chain Rule

dy/dx = (dy/du) × (du/dx) · Trigonometric Derivatives · d/dx(sin x) = cos x · d/dx(cos x) = -sin x · d/dx(tan x) = sec2 x · d/dx(sec x) = sec x tan x · Exponentials and Logarithms · d/dx(ex) = ex · d/dx(ln x) = 1/x · 5. Applications (Lessons 21-22)

Newton's Method: xn+1 = xn - f(xn) / f'(xn) Tangent Line Equation: y - f(x0) = f'(x0)(x - x0)

MTH101 Handouts Summary - Lessons 1 to 22