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Calculus of a Single Variable
- A function value f(a) is a relative ________ of f when there exists an interval (x1, x2) containing a such that x1 < x < x2 implies f(a) ≥ f(x).arrow_forwardmathmatics advanced Give an example of an everywhere-defined real function that is continuous at exactly three pointsarrow_forward(a) Sketch the graph of y = f(x), given the following: • f(−1) = 2; f(0) = 3; lim x→−∞ f(x) = 1; lim x→∞ f(x) = 0; lim x→1−f(x) = −∞; lim x→1+f(x) =+∞ • f0(0) = 0; f0(x) > 0 for x ∈ (−∞,0); f0(x) < 0 for x ∈ (0,1)∪(1,∞) • f00(−1) = 0; f00(x) < 0 for x ∈ (−1,1); f00(x) > 0 for x ∈ (−∞,−1)∪(1,∞)arrow_forward
- Sketch the graph of a function y = f(x) with all of the following properties: a) f ′(x) > 0 for −2 ≤ x < 1 b) f ′(2) = 0 c) f ′(x) > 0 for x > 2 d) f(2) = 2 and f(0) = 1 e) lim x → −∞ f(x) = 0 and lim x → ∞ f(x) = ∞ f) f ′(1) does not existsarrow_forwardLet f(x)=2x+1 and g(x)=x2-1. What is the composition (f of g)(x)?arrow_forwarda = 0 x −0.1 −0.01 −0.001 −0.0001 0 0.0001 0.001 0.01 0.1 f(x) 19.0303 −3.00303 −3.0003 −3.00003 0 3.00003 3.0003 3.00303 3.0303 (a) lim x→a− f(x) (b) lim x→a+ f(x)arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage