# Calculus 1: Newton Raphson Method

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All Calculus 1LimitsDefinition of the DerivativeProduct and Quotient RulePower Rule and Basic DerivativesDerivatives of Trig FunctionsExponential and Logarithmic FunctionsChain RuleInverse and Hyperbolic Trig DerivativesImplicit DifferentiationRelated Rates ProblemsLogarithmic DifferentiationGraphing and Critical PointsOptimization ProblemsIndeterminate Forms and l'Hospital's RuleLinear Approximation and DifferentialsNewton Raphson MethodIndefinite IntegralsU SubstitutionDefinite Integrals and Fundamental TheoremApplications of Integration

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Use Newton's method for approximating roots of functions to approximate $\sqrt{0.99}$

Use the Newton Raphson method to approximate the real zero close to $x = 1$ until two successive approximations differ by less than 0.005 for the following function

$f(x) = 2x^2 - 3$

Starting with an initial value $x_1 = 1$, perform 2 iterations of Newton's Method on $f(x) = x^3 - x - 1$ to approximate the root.

Use Newton's Method to approximate the solution to the following equation

$\cos{(x)} = \frac{x}{5}$

Use Newton's Method to approximate a solution to $2\cos{(x)} = 3x$ (Let $x_0 = \frac{\pi}{6}$ and find $x_2$)