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Chapter 1: Q. 37 (page 149)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

We have:

$\lim_{x 鈫� 鈭�} (2 x^{- \frac{4}{3}})$

02

Step 2. Solve the limits.

The function is $\lim_{x 鈫� 鈭�} (2 x^{- \frac{4}{3}})$ .

$\lim_{x 鈫� a} [c 路 f (x)] = c 路 \lim_{x 鈫� a} f (x) = 2 路 \lim_{x 鈫� 鈭� 鈥�} (x^{- \frac{4}{3}}) \lim_{x 鈫� a} {[f (x)]}^{b} = {[\lim_{x 鈫� a} f (x)]}^{b} = 2 {(\lim_{x 鈫� 鈭� 鈥�} (x))}^{- \frac{4}{3}} = 2 {鈭�}^{- \frac{4}{3}} = 0$

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Most popular questions from this chapter

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

$\lim_{x 鈫� 2} \frac{x^{2} - 3 x + 2}{x - 2} = 1$

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

$\lim_{x 鈫� 2^{+}} 3 \sqrt{2 x - 4} = 0$

Find a formula for the cost $C (r)$ of producing a gourmet soup can with radius $r$ and height $5$ inches, and answer the following questions:

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Your manager wants you to produce $5$ -inch-tall cans that cost between $20$ and $40$ cents. Write this requirement as an absolute value inequality.
What range of radii would satisfy your manager? Write an absolute value inequality whose solution set lies inside this range of radii.

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

$\lim_{x 鈫� - 1} 6 .$

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