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((3+2*x)/(1+x))^x

Limit of the function ((3+2*x)/(1+x))^x

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              x
     /3 + 2*x\ 
 lim |-------| 
x->oo\ 1 + x / 
limx(2x+3x+1)x\lim_{x \to \infty} \left(\frac{2 x + 3}{x + 1}\right)^{x}
Limit(((3 + 2*x)/(1 + x))^x, x, oo, dir='-')
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
02468-8-6-4-2-101002000
Rapid solution [src]
oo
\infty
Other limits x→0, -oo, +oo, 1
limx(2x+3x+1)x=\lim_{x \to \infty} \left(\frac{2 x + 3}{x + 1}\right)^{x} = \infty
limx0(2x+3x+1)x=1\lim_{x \to 0^-} \left(\frac{2 x + 3}{x + 1}\right)^{x} = 1
More at x→0 from the left
limx0+(2x+3x+1)x=1\lim_{x \to 0^+} \left(\frac{2 x + 3}{x + 1}\right)^{x} = 1
More at x→0 from the right
limx1(2x+3x+1)x=52\lim_{x \to 1^-} \left(\frac{2 x + 3}{x + 1}\right)^{x} = \frac{5}{2}
More at x→1 from the left
limx1+(2x+3x+1)x=52\lim_{x \to 1^+} \left(\frac{2 x + 3}{x + 1}\right)^{x} = \frac{5}{2}
More at x→1 from the right
limx(2x+3x+1)x=0\lim_{x \to -\infty} \left(\frac{2 x + 3}{x + 1}\right)^{x} = 0
More at x→-oo
The graph
Limit of the function ((3+2*x)/(1+x))^x