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Chapter 1: Q. 51 (page 88)

Use tables of values to make educated guesses for each of the limits in Exercises 39–52.
$\lim_{x \to \infty} \sin x$

Short Answer

Expert verified

The limit does not exist.

Step by step solution

Step 1. Given Information.

The given function is $\lim_{x \to \infty} \sin x .$

Step 2. Value of the limit.

Consider the table,

$x$	$10$	$100$	$1000$
$\sin x$	$- 0.544$	$- 0.506$	$0.8268$

The value approaches to $\infty$ as $x \to \infty$ ,

Therefore,

The limit does not exist.

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Most popular questions from this chapter

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 $x \in (c - δ, c) \cup (c, c + δ) then f (x) \in (L - ε, L + ε)$

$\underset{x \to - 1}{l i m} \frac{x^{2} - 2 x - 3}{x + 1} = - 4, ε = 0.1$

For each limit statement , use algebra to find δ > 0 in terms of $ε$ > 0 so that if 0 < |x − c| < δ, then | f(x) − L| < $ε$ .

$\lim_{x \to - 2} (4 - 2 x) = 8$

$\lim_{x \to 1} \frac{1 - \cos (x - 1)}{x}$

Write each of the inequalities in interval notation:

$0 < | x + 3 | < 0.05$

Write a delta–epsilon proof that proves that $f$ is continuous on its domain. In each case, you will need to assume that δ is less than or equal to $1$ .

$f (x) = x^{- 1 / 2}$

See all solutions

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Use tables of values to make educated guesses for each of the limits in Exercises 39–52.limx→∞sinx

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Value of the limit.

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Most popular questions from this chapter

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Use tables of values to make educated guesses for each of the limits in Exercises 39–52.
$\lim_{x \to \infty} \sin x$