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Chapter 1: Q. 52 (page 149)

Calculate each limit in Exercises 35–80.
$\lim_{x \to \infty} (x^{- \frac{1}{3}} - x^{- \frac{1}{2}})$

Short Answer

Expert verified

The limit is 0.

Step by step solution

01

Step 1. Given Information:

Given expression:

$\lim_{x \to \infty} (x^{- \frac{1}{3}} - x^{- \frac{1}{2}})$

We want to calculate the value of expression.

02

Step 2. Solution:

Since $- \frac{1}{3} a n d - \frac{1}{2}$ are negative power, as localid="1648226025692" $x \to \infty$ we have $x^{- \frac{1}{3}} \to 0 a n d x^{- \frac{1}{2}} \to 0$

Therefore the limit is $0 - 0 = 0$

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Most popular questions from this chapter

Calculate each of the limits:

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

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

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

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

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$\lim_{x \to 4} (6 x - 1) = 23$ .

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

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

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