Mister Exam

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

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              x
     /3 + 2*x\ 
 lim |-------| 
x->oo\ 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

Plot the graph

Rapid solution [src]

oo

\infty

Expand and simplify

Other limits x→0, -oo, +oo, 1

\lim_{x \to \infty} \left(\frac{2 x + 3}{x + 1}\right)^{x} = \infty

\lim_{x \to 0^-} \left(\frac{2 x + 3}{x + 1}\right)^{x} = 1

\lim_{x \to 0^+} \left(\frac{2 x + 3}{x + 1}\right)^{x} = 1

\lim_{x \to 1^-} \left(\frac{2 x + 3}{x + 1}\right)^{x} = \frac{5}{2}

\lim_{x \to 1^+} \left(\frac{2 x + 3}{x + 1}\right)^{x} = \frac{5}{2}

\lim_{x \to -\infty} \left(\frac{2 x + 3}{x + 1}\right)^{x} = 0

The graph