find lim x --> +infinity of f(x) = 5x / (x^2 + 5)^(1/2)

[mathhelp]

find the lim x --> positive infinity of f(x) = 5x / (x^2 + 5)^(1/2)

thanks

 

[arthur ohlsten]

y=5x/[x^2+5]^1/2 lim x-->+oo
lim y = oo/oo omdefined by L'Hospitals rule
lim y = 5/{1/2[x+2+5][2x]}
lim y x-->oo =0 answer

Arthur

 

[mathhelp]

y=5x/[x^2+5]^1/2 lim x-->+oo
lim y = oo/oo omdefined by L'Hospitals rule
lim y = 5/{1/2[x+2+5][2x]}
lim y x-->oo =0 answer

Arthur

the bolded content does not make sense

 

[galactus]

\(\displaystyle \L\\\lim_{x\to+\infty}\frac{5x}{\sqrt{x^{2}+5}}\)

\(\displaystyle \L\\\lim_{x\to+\infty}\frac{\frac{5x}{x}}{\frac{\sqrt{x^{2}+5}}{\sqrt{x^{2}}}\)

=\(\displaystyle \L\\\lim_{x\to+\infty}\frac{5}{\sqrt{1+\frac{5}{x^{2}}}}\)

Now, see what the limit is?.

 

[arthur ohlsten]

my answer was wrong
I made a error in the derivative

another approach
y=5x/[x^2+5]^1/2 expand denominator
y=5x/[x^2+10x+25]^1/2 devide numerator and denominator by x
y=5/[1+10/x +(5/x)^2 ]^ 1/2 let x-->+oo
y=5/1
y=5 answer

sorry for the error der. of [x^2+5]^1/2 = 1/2 [x^2+5]^-1/2 [2x]
I left out ^-1/2

Arthur

 

[mathhelp]

\(\displaystyle \L\\\lim_{x\to+\infty}\frac{5x}{\sqrt{x^{2}+5}}\)

\(\displaystyle \L\\\lim_{x\to+\infty}\frac{\frac{5x}{x}}{\frac{\sqrt{x^{2}+5}}{\sqrt{x^{2}}}\)

=\(\displaystyle \L\\\lim_{x\to+\infty}\frac{5}{\sqrt{1+\frac{5}{x^{2}}}}\)

Now, see what the limit is?.

Is it right that the answer to the limit is 5/infty =infty?

 

[galactus]

Look again. That isn't 5/infinity