Solving Equations Numerically flashcards

6 practice cards drawn from the Solving Equations Numerically lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.

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Iterating xₙ₊₁ = (xₙ² + 1)/6 from x₀ = 3, what is x₂?

0.6296

from “Solving Equations by Iteration”

Iterating xₙ₊₁ = (xₙ² + 4)/4 from x₀ = 3, what is x₂?

3.6406

from “Solving Equations by Iteration”

f(x) = x² − 8 with x₀ = 3. What is x₁, to 4 decimal places?

2.8333

from “The Newton-Raphson Method”

f(x) = x² − 5 with x₀ = 3. What is x₁, to 4 decimal places?

2.3333

from “The Newton-Raphson Method”

A tangent is nearly flat at the guess. What happens to the next guess?

it lands far from the root

from “When Newton-Raphson Fails”

f(x) = x³ − 2x + 2 with x₀ = 0. What is x₂?

0

from “When Newton-Raphson Fails”

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