Category: 0. BLOG

For bisection on [a,b] with tolerance ε, which inequality gives the minimum n ensuring interval length ≤ ε? A 2ⁿ

When comparing two methods, which one is said to converge faster near the root if its error drops more quickly?

A sequence {xₙ} is said to converge to L when xₙ approaches: A 0 always B Infinity only C L

While iterating for a root, what does a “tolerance” mainly represent in practice? A Exact root value B Function maximum

Which error comes from chopping an infinite process in computations? A Round-off error B Relative error C Truncation error D

Let S = {1 − 1/n : n∈ℕ}. What is sup S? A 0 B 2 C 1 D No

Let S = {x ∈ ℝ : x² < 2}. What is sup S? A −√2 B 1 C 2

Which statement correctly describes the interval [a, b)? A a included only B Both excluded C Both included D b

On the real line, which inequality shows x is to the left of y? A x ≥ y B x

Which set equals the real line ℝ? A All rational numbers B All complex numbers C All real numbers D