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2D Distance & Line Geometry Distance between points, point-to-line distance, slope, and angle Point 1 (x₁, y₁): Point 2 (x₂,

Conic Sections Calculator Ellipse · Hyperbola · Parabola Conic Type:Ellipse: (x-h)²/a² + (y-k)²/b² = 1Hyperbola: (x-h)²/a² – (y-k)²/b² = 1Parabola:

Rational Root Theorem Possible rational roots = ±(factors of constant) / (factors of leading coeff) Polynomial (e.g., x^3 – 6x^2

Taylor Series Expansion f(x) ≈ Σ f^(n)(a)/n! · (x-a)^n Function f(x):sin(x)Center a =Order n =Expand Series Expansion

Partial Fractions Decomposition Break rational functions into simpler parts Rational function P(x)/Q(x):(x+2)/(x^2-1)Decompose Decomposition Method: 1. Factor denominator2. Set up partial

ODE Solver dy/dx = f(x,y) dy/dx = -y Initial condition y(x0) = Solve ODE Solution General solution: Method: Separation of

Integration by Substitution u-substitution guide Integral to solve: (2x)*(x^2+1)^5 Guide Substitution Suggested u-substitution Let u = Then du = Steps:

Derivative Calculator (Advanced) Product Rule · Quotient Rule · Chain Rule Function f(x): (x^2)*(sin(x)) Evaluate derivative at x = (optional):