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Chapter 1: Q. 18 (page 153)

Limits of basic functions: Fill in the blanks to complete the limit rules that follow. You may assume that k is positive.
$\lim_{x \to 0} {(1 + x)}^{\frac{1}{x}} =______$

Short Answer

Expert verified

The value of the limit is $\lim_{x \to 0} {(1 + x)}^{\frac{1}{x}} = e .$

Step by step solution

Step 1. Given Information.

The given limit function is $\lim_{x \to 0} {(1 + x)}^{\frac{1}{x}} .$

Step 2. Filling the blank.

To fill in the blank, apply the common limit.

So,

$\lim_{x \to 0} {(1 + x)}^{\frac{1}{x}} = e$

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Most popular questions from this chapter

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

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$If x > N, then 1 - 2 x < - 500$

For each limit statement in Exercises $41 - 44$ , use algebra to find $δ$ or $N$ in terms of $ε$ or $M$ , according to the appropriate formal limit definition.

$\lim_{x \to 1^{-}} \frac{1}{1 - x} = \infty$ , find $δ$ in terms of $M$ .

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Limits of basic functions: Fill in the blanks to complete the limit rules that follow. You may assume that k is positive.limx→01+x1x=______

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Filling the blank.

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Most popular questions from this chapter

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Limits of basic functions: Fill in the blanks to complete the limit rules that follow. You may assume that k is positive.
$\lim_{x \to 0} {(1 + x)}^{\frac{1}{x}} =______$