Chapter 1: Q. 21 (page 149)

$\infty^{0}$ that approaches (a) $1,$ (b) $2,$ (c) $\infty .$

Short Answer

Expert verified

$\infty^{0}$ approaches to (a) $1 .$

Step by step solution

Step 1. Given information

The given information is $\infty^{0}$ , we need to write $\infty^{0}$ approaches to (a) $1,$ (b) $2,$ (c) $\infty .$

Step 2. The explanation for the correct option

For example, $\lim_{x \to \infty} (x^{\frac{1}{x}}) .$

$= \lim_{x \to \infty} {(e^{\ln x})}^{\frac{1}{x}} .$

$= \lim_{x \to \infty} (e^{\frac{\ln x}{x}}) .$

$= e (\lim_{x \to \infty} e^{\frac{\ln x}{x}}) .$

$= e^{\lim_{x \to \infty} \frac{\frac{1}{x}}{1} .}$ (Applying the L-Hospital rule).

$= e^{0} .$

$= 1 .$

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$\infty^{0}$ that approaches (a) $1,$ (b) $2,$ (c) $\infty .$

Short Answer

Step by step solution

Step 1. Given information

Step 2. The explanation for the correct option

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∞0that approaches (a)1,(b)2,(c)∞.

Short Answer

Step by step solution

Step 1. Given information

Step 2. The explanation for the correct option

One App. One Place for Learning.

Most popular questions from this chapter

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$\infty^{0}$ that approaches (a) $1,$ (b) $2,$ (c) $\infty .$