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 ( 67+ )
Otras preguntas
A rocket is launched from the ground. The function h(t)= -4.9t^2 +180t models the height of a rocket launcher from the ground t seconds after it is launched.
@stewyWhich sentence uses a verb that agrees with its compound subject? A.Waiters and waitresses serve the diners at the banquet.B.cell phones and tablets i
what do this mean explain the following thoughts of annemarie, "it was hard for the ones who were waiting, Annemarie knew. Less dangerous perhaps but more fear
how did jazz demonstrate the independent spirit of the times?
What is the interquartile range of the data set below? Growth in feet of oak trees: 68,80,73,90,120,94,76,112,101,94,72(1) 22 (2) 28
A radio station transmits waves at a frequency of 120MHz an a speed of 300 million m/s. Calculate the wavelength.
which state capital is north of 40 degrees north latitude: Frankfort, denver, salt lake city, or columbus?
What what handels full name
What is the interquartile range of the data set below? Growth in feet of oak trees: 68,80,73,90,120,94,76,112,101,94,72(1) 22 (2) 28
Which sentence uses a verb that agrees with its subject?A.In a dark corner of the attic were many unopened boxes.B.Across the surface of the water glides swans.
