For each whole number n, explain why there exists x with (2n − 1)π/2 < x < (2n + 1)π/2 such that tan(x) = x. Problem 2. For all x ∈ (0, ∞), define f(x) = (1 + x)1/x. Write a table of values of f (x) for x = 1, 10, 100, 1000, and guess limx→∞ f (x). If the limit exists, explain why it must be ≥ 1

For each whole number n, explain why there exists x with (2n − 1)π/2 < x < (2n + 1)π/2 such that tan(x) = x. Problem 2. For all x ∈ (0, ∞), define f(x) = (1 + x)1/x. Write a table of values of f (x) for x = 1, 10, 100, 1000, and guess limx→∞ f (x). If the limit exists, explain why it must be ≥ 1

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

For each whole number n, explain why there exists x with (2n − 1)π/2 < x < (2n + 1)π/2 such that tan(x) = x.

Problem 2. For all x ∈ (0, ∞), define f(x) = (1 + x)1/x. Write a table of values of f (x) for x = 1, 10, 100, 1000, and guess limx→∞ f (x). If the limit exists, explain why it must be ≥ 1

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