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2.46 Let Q(x) = Vr. Prove that the function Q is uniformly continuous on [0, o). (Hint: See Exercise 2.21.) For Reference 2.21 † Let Q(x) = VT, which is defined for all x > 0. Prove: QE C[0, ∞0). (Hint: If a > 0, and e > 0, we seek 8 > 0 such that x > 0 and |x – a| < ô implies |Q(x) – Q(a)| < e. Begin by showing that |VE – Val < lx – a|.) %3!

2.46 Let Q(x) = Vr. Prove that the function Q is uniformly continuous on [0, o). (Hint: See Exercise 2.21.) For Reference 2.21 † Let Q(x) = VT, which is defined for all x > 0. Prove: QE C[0, ∞0). (Hint: If a > 0, and e > 0, we seek 8 > 0 such that x > 0 and |x – a| < ô implies |Q(x) – Q(a)| < e. Begin by showing that |VE – Val < lx – a|.) %3!

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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2.46 Let Q(x) = Vr. Prove that the function Q is uniformly continuous on [0, 0). (Hint: See Exercise 2.21.) For Reference 2.21 † Let Q(x) Vx, which is defined for all x > 0. Prove: Q E C0, 0). (Hint: If a > 0, and e > 0, we seek 8 > 0 such that x >0 and |x – a| < 6 implies |Q(x) – Q(a)| < e. Begin by showing that |VT – val < |x – al.)
Transcribed Image Text:2.46 Let Q(x) = Vr. Prove that the function Q is uniformly continuous on [0, 0). (Hint: See Exercise 2.21.) For Reference 2.21 † Let Q(x) Vx, which is defined for all x > 0. Prove: Q E C0, 0). (Hint: If a > 0, and e > 0, we seek 8 > 0 such that x >0 and |x – a| < 6 implies |Q(x) – Q(a)| < e. Begin by showing that |VT – val < |x – al.)
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