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Chapter 1: Q. 11 (page 153)

Limits of basic functions: Fill in the blanks to complete the limit rules that follow. You may assume that k is positive
$\lim_{x \to \infty} 2^{x}$ =?.

Short Answer

Expert verified

The value of the limit is $\infty$ .

Step by step solution

01

Step 1. Given Information.

The given limit function is $\lim_{x \to \infty} 2^{x}$ .

02

Step 2. Value of the limit.

The given limit can be written as,

$= \lim_{x \to \infty} 2^{x} = 2^{\infty} = \infty$

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Most popular questions from this chapter

Calculate each of the limits:

$\lim_{h \to 0} \frac{{(1 + h)}^{3} - 1^{3}}{h}$ .

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

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

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

$\lim_{x \to 2} (3 - 4 x) = - 5$ .

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.

Calculate each of the limits:

$\lim_{x \to 1} x \sin^{- 1} \frac{x}{2}$ .

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