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Chapter 1: Q. 37 (page 149)

Calculate each limit in Exercises 35-80.
$\lim_{x \to \infty} (2 x^{- \frac{4}{3}})$

Short Answer

Expert verified

The limit of the function is $\lim_{x \to \infty} (2 x^{- \frac{4}{3}}) = 0$ .

Step by step solution

01

Step 1. Given information.

We have:

$\lim_{x \to \infty} (2 x^{- \frac{4}{3}})$

02

Step 2. Solve the limits.

The function is $\lim_{x \to \infty} (2 x^{- \frac{4}{3}})$ .

$\lim_{x \to a} [c \cdot f (x)] = c \cdot \lim_{x \to a} f (x) = 2 \cdot \lim_{x \to \infty} (x^{- \frac{4}{3}}) \lim_{x \to a} {[f (x)]}^{b} = {[\lim_{x \to a} f (x)]}^{b} = 2 {(\lim_{x \to \infty} (x))}^{- \frac{4}{3}} = 2 \infty^{- \frac{4}{3}} = 0$

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Most popular questions from this chapter

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

For each functionf graphed in Exercises23–26, describe the intervals on whichf is continuous. For each discontinuity off, describe the type of discontinuity and any one-sided continuity. Justify your answers about discontinuities with limit statements.

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.

$\lim_{x \to - 5} \sqrt{x} .$

What are punctured intervals, and why do we need to use them when discussing limits?

In Exercises 39–44, use Theorem 1.16 and left and right limits to determine whether each function f is continuous at its break point(s). For each discontinuity of f, describe the type of discontinuity and any one-sided discontinuity.

$f (x) = \{\begin{array}{l} (x - 3), i f x < 0 \\ - (x - 3), i f x ⩾ 0 \end{array} .$

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