Reem
Reem
01-02-2015
Mathematics
contestada
Calculate the following limit:
Respuesta :
konrad509
konrad509
01-02-2015
[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]
Answer Link
VER TODAS LAS RESPUESTAS ( 11+ )
Otras preguntas
Narine is solving the equation √3q=6 for q. Her work is shown A=6 B=2 A=9 B=3 A=12 B=4 A=36 B=12
If f(x) = -x + 8 and g(x) = x^4, what is (gºf)(2)?
The change from one number to the next in a geometric sequence is called the: A. common difference. B. arithmetic difference. C. common ratio. D. geometric rati
Which of the following is the measure of AXYif ray xy bisects AXB, which measures 110°
Write a recursive formula for the sequence -2,4,-8, 16, ... a = -2, a, = an - 1+6, n22 a = -2, an=-2an - 1, n > 2 19,5-2, a, = 24, -1, 122 aj = 16, an= -2an
What are the coordinates of the vertices of the image of rectangle WXYZ after the transformation Ro 90°(x, y)? W'(-4,-1) X' Y' Z'(-4, 2)
Davison Company determined that the book basis of its net accounts receivable was less than the tax basis of its net accounts receivable by $800,000 due to a di
Which formatting or design feature can help create a mood? arrangement capitals fonts numbers
И показалась комета и выступил Лала-паша августа 7. Месхи отдали крепости и Манучар явился к нему, поднес крепости. Ушел [Лала-паша] в Тбилиси, Дауд-хан сжег Тб
Mr de guzman bought 7 1/2 of meat.He used 2 3/4 for afritada,3 1/8 kg for menudo and the rest for pochero.How many kilograms of meat did he used for pochero?
