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If f(x) is Lipschitz with constant L and |f(x)| < B, then [f(x)]² is Lipschitz with constant 2LB.

If f(x) is Lipschitz with constant L and |f(x)| < B, then [f(x)]² is Lipschitz with constant 2LB.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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1. Determine if the following statements are TRUE or FALSE, and justify your answer (e.g. a short proof or counter-example, refer to a theorem, etc). a) If f(x) is Lipschitz with constant L and |f(x)| < B, then [f(x)]² is Lipschitz with constant 2LB. b) Consider data points (x;, Yi) and assume they fit the model y(x) parameter a can then be estimated by the slope in a log-log plot of the points. c) Consider two n-by-n matrices A, U, where A is general but U is upper-triangular (with positive diagonal entries). The total operation count of computing the matrix-vector product Ax is lower than solving the linear system Ux backward substitution, for some vectors x,b. b. a". The b using a b 0 d) The matrix A: ba b is positive definite if and only if a > 0 and |b| < a/V2. 0 b a
Transcribed Image Text:1. Determine if the following statements are TRUE or FALSE, and justify your answer (e.g. a short proof or counter-example, refer to a theorem, etc). a) If f(x) is Lipschitz with constant L and |f(x)| < B, then [f(x)]² is Lipschitz with constant 2LB. b) Consider data points (x;, Yi) and assume they fit the model y(x) parameter a can then be estimated by the slope in a log-log plot of the points. c) Consider two n-by-n matrices A, U, where A is general but U is upper-triangular (with positive diagonal entries). The total operation count of computing the matrix-vector product Ax is lower than solving the linear system Ux backward substitution, for some vectors x,b. b. a". The b using a b 0 d) The matrix A: ba b is positive definite if and only if a > 0 and |b| < a/V2. 0 b a
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