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2+((5-x)/(6-x))^x
Limit of the function/ 2+((5-x)/(6-x))^x

Limit of the function 2+((5-x)/(6-x))^x

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     /           x\
     |    /5 - x\ |
 lim |2 + |-----| |
x->oo\    \6 - x/ /
lim⁡x→∞((5−x6−x)x+2)\lim_{x \to \infty}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) 
Limit(2 + ((5 - x)/(6 - 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
02468-8-6-4-2-10100200000
Plot the graph
Rapid solution [src] 
2 + E
2+e2 + e
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞((5−x6−x)x+2)=2+e\lim_{x \to \infty}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = 2 + e
lim⁡x→0−((5−x6−x)x+2)=3\lim_{x \to 0^-}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = 3
More at x→0 from the left
lim⁡x→0+((5−x6−x)x+2)=3\lim_{x \to 0^+}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = 3
More at x→0 from the right
lim⁡x→1−((5−x6−x)x+2)=145\lim_{x \to 1^-}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = \frac{14}{5}
More at x→1 from the left
lim⁡x→1+((5−x6−x)x+2)=145\lim_{x \to 1^+}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = \frac{14}{5}
More at x→1 from the right
lim⁡x→−∞((5−x6−x)x+2)=2+e\lim_{x \to -\infty}\left(\left(\frac{5 - x}{6 - x}\right)^{x} + 2\right) = 2 + e
More at x→-oo
The graph
Limit of the function 2+((5-x)/(6-x))^x
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