Chapter 1: Q. 19 (page 149)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

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

Step 2. The explanation for the correct option

For example, $\lim_{x \to 0^{+}} x^{x}$

$= \lim_{x \to 0} e^{\ln z^{x}}$

$= \lim_{x \to 0} e^{x \ln x}$

$= \lim_{x \to 0} e^{\frac{\ln x}{\frac{1}{x}}}$

$= \lim_{x \to 0} \frac{\frac{1}{x}}{- \frac{1}{x^{2}}}$

$= \lim_{x \to 0} e^{\frac{1}{x} \cdot - x^{2}}$

$= \lim_{x \to 0} e^{- x}$

$= e^{0}$

$= 1$

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. The explanation for the correct option

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00that approaches (a)1,(b)0,(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

Recommended explanations on Math Textbooks

Mechanics Maths

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

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