Calculate the following limit:

Question

01-02-2015
Mathematics

Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Calculate the following limit:

Sagot :

We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.

Carly and Simon are renting formal clothes for a wedding. They found a rental company that charges a fixed fee of $100 plus an additional fee of $40 per hour. I

inside a volcano how do the slanted layers of hardened lava get there

Please help!!!!!!!!!!!! 1) You have $20 in savings at the bank.Each week,you add $2 to your savings Let y represent the total amount of money you have saved at

Which of these sentences is punctuated correctly? I need to leave for school right now; because I don't have all of my school supplies gathered. I need to leave

Which words in the sentence are the complete adjective clause? The time when I felt worst was the day of that long drive. A. the time when I felt worst B. when

The development of the cell theory involved ___________________________. A. different ideas from different scientists. B. the efforts of one scientist. C. work

Who helped disprove the idea of spontaneous generation by demonstrating that maggots come from fly eggs and NOT from meat? A. Francesco Redi B. John Needham C.

Help Please! Write each repeating decimal using bar notation. 1) 0.999... 2) 5.92111... 3) 2.010101... 4) 13.1464646... 5) 26.993993... 6) 30.6841841841... Writ

Find the best word to complete the sentence. 5. After several skateboarders were injured on Main Street, the city council issued a(n) ___ for tighter downtown t

Which sentence contains an adverb clause? A. When do the tryouts for the dance team begin? B. You should mark your calendar for the family picnic next month. C.

konrad509 konrad509 · Answer 1 · 2015-02-01T06:55:30-05:00

[tex]\lim_{x\to\infty}\dfrac{\sqrt x}{\sqrt{x+\sqrt{x+\sqrt x}}}=\\ \lim_{x\to\infty}\dfrac{\dfrac{\sqrt x}{\sqrt x}}{\dfrac{\sqrt{x+\sqrt{x+\sqrt x}}}{\sqrt x}}=\\ \lim_{x\to\infty}\dfrac{1}{\sqrt{\dfrac{x+\sqrt{x+\sqrt x}}{x}}}=\\ \lim_{x\to\infty}\dfrac{1}{\sqrt{1+\dfrac{\sqrt{x+\sqrt x}}{x}}}=\\ \lim_{x\to\infty}\dfrac{1}{\sqrt{1+\dfrac{\sqrt{x+\sqrt x}}{\sqrt{x^2}}}}=\\[/tex]
[tex]\lim_{x\to\infty}\dfrac{1}{\sqrt{1+\sqrt{\dfrac{x+\sqrt x}{x^2}}}}=\\\lim_{x\to\infty}\dfrac{1}{\sqrt{1+\sqrt{\dfrac{1}{x}+\dfrac{\sqrt x}{\sqrt{x^4}}}}}=\\\lim_{x\to\infty}\dfrac{1}{\sqrt{1+\sqrt{\dfrac{1}{x}+\sqrt{\dfrac{x}{x^4}}}}}=\\ \lim_{x\to\infty}\dfrac{1}{\sqrt{1+\sqrt{\dfrac{1}{x}+\sqrt{\dfrac{1}{x^3}}}}}=\\ =\dfrac{1}{\sqrt{1+\sqrt{0+\sqrt{0}}}}=\\[/tex]
[tex]=\dfrac{1}{\sqrt{1+0}}=\\ =\dfrac{1}{\sqrt{1}}=\\ =\dfrac{1}{1}=\\ 1 [/tex]

Sagot :

Other Questions