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Chapter 1: Q. 30 (page 153)

Find the limit by hand.
$\lim_{x \to \infty} \sin \frac{1}{x}$

Short Answer

Expert verified

On solving the limit, we get, $0$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$\lim_{x \to \infty} \sin \frac{1}{x}$

Step 2. Solve the given limit.

Using the limits,

$= \sin \frac{1}{\infty} = \sin 0 = 0$

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Most popular questions from this chapter

Write delta-epsilon proofs for each of the limit statements in Exercises $47 - 60 .$

$\lim_{x \to 5^{+}} \sqrt{x - 5} = 0$

Write delta-epsilon proofs for each of the limit statements $\lim_{x \to c} f (x) = L$ in Exercises $47 - 60$ .

$\lim_{x \to 1} (2 x^{2} - 4 x + 3) = 1$ .

For each limit $\underset{x \to c}{l i m} f (x) = L$ in Exercises 43–54, use graphs and algebra to approximate the largest value of $δ$ such that if localid="1648023101818" $x \in (c - δ, c) \cup (c, c + δ) then f (x) \in (L - ε, L + ε)$

localid="1648023199049" role="math" $\underset{x \to - 1}{l i m} \frac{x^{2} - 2 x - 3}{x + 1} = - 4, ε = 1$

Write delta-epsilon proofs for each of the limit statements $\lim_{x \to c} f (x) = L$ in Exercises $47 - 60$ .

$\lim_{x \to 3} (x^{2} - 6 x + 11) = 2$ .

For each of the following sign charts, sketch the graph of a function f that has the indicated signs, zeros, and discontinuities:

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Find the limit by hand.limx→∞sin1x

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the given limit.

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Most popular questions from this chapter

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Find the limit by hand.
$\lim_{x \to \infty} \sin \frac{1}{x}$