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Chapter 1: Q. 50 (page 136)

$\lim_{x 鈫� 0 +} (l n (1 + \sqrt{x}))$

Short Answer

Expert verified

$\lim_{x 鈫� 0 +} (l n (1 + \sqrt{x})) = 0$

Step by step solution

Step 1. Given information

$\lim_{x 鈫� 0 +} (l n (1 + \sqrt{x}))$

Step 2. Plug in the values

$\lim_{x 鈫� 0 +} (l n (1 + \sqrt{x})) = \ln (1 + \sqrt{x})$

$\lim_{x 鈫� 0 +} (l n (1 + \sqrt{x})) = \ln (1 + \sqrt{0})$

$\lim_{x 鈫� 0 +} (l n (1 + \sqrt{x})) = 0$

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Most popular questions from this chapter

For each limit statement , use algebra to find 未 > 0 in terms of $蔚$ > 0 so that if 0 < |x 鈭� c| < 未, then | f(x) 鈭� L| < $蔚$ .

$\lim_{x 鈫� 1} 2 x^{4} = 2; you may assume 未鈮� 1$ .

If $f$ is a continuous function, what can you say about $\lim_{x 鈫� 1} f (x) ?$

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

$\lim_{x 鈫� 8} (3 x - 11) = 13$ .

Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Extreme Value Theorem, and illustrate on your graph that the conclusion of the Extreme Value Theorem does not necessarily hold.

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

$\lim_{x 鈫� 1} (2 x + 4) = 6$ .

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limx鈫�0+ln1+x

Short Answer

Step by step solution

Step 1. Given information

Step 2. Plug in the values

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Most popular questions from this chapter

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$\lim_{x 鈫� 0 +} (l n (1 + \sqrt{x}))$