Chapter 7: Q. 59 (page 604)

Evaluate the limits in Exercises 55–60. Use the theorems in this section to justify each step of your work.
$\lim_{x \to \infty} \sqrt{k^{2} + k} - k$

Short Answer

Expert verified

$\lim_{x \to \infty} \sqrt{k^{2} + k} - k = \frac{1}{2}$

Step by step solution

Step 1. Given information

$\lim_{x \to \infty} \sqrt{k^{2} + k} - k$

Step 2. Calculate the limit

$\lim_{x \to \infty} \sqrt{k^{2} + k} - k = \lim_{x \to \infty} (\frac{1}{\sqrt{1 + \frac{1}{x}} + 1})$

$\lim_{x \to a} [\frac{f (x)}{g (x)}] = \frac{\lim_{x \to a} f (x)}{\lim_{x \to a} g (x)}, \lim_{x \to a} g (x) \neq 0$

role="math" localid="1649174927444"

\lim_{x \to \infty} \sqrt{k^{2} + k} - k = \frac{\lim_{x \to \infty} (1)}{\lim_{x \to \infty} (\sqrt{1 + \frac{1}{x}} + 1)}

\lim_{x \to \infty} \sqrt{k^{2} + k} - k = \frac{1}{2}

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Evaluate the limits in Exercises 55–60. Use the theorems in this section to justify each step of your work.
$\lim_{x \to \infty} \sqrt{k^{2} + k} - k$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculate the limit

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Evaluate the limits in Exercises 55–60. Use the theorems in this section to justify each step of your work. limx→∞k2+k-k

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculate the limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Evaluate the limits in Exercises 55–60. Use the theorems in this section to justify each step of your work.
$\lim_{x \to \infty} \sqrt{k^{2} + k} - k$