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

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

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      /     -x\
 lim  \2 + 3  /
x->-1+
lim⁡x→−1+(2+(13)x)\lim_{x \to -1^+}\left(2 + \left(\frac{1}{3}\right)^{x}\right) 
Limit(2 + (1/3)^x, x, -1)
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
-2.0-1.5-1.0-0.52.00.00.51.01.5020
Plot the graph
Rapid solution [src] 
5
55
Expand and simplify
One‐sided limits [src] 
      /     -x\
 lim  \2 + 3  /
x->-1+
lim⁡x→−1+(2+(13)x)\lim_{x \to -1^+}\left(2 + \left(\frac{1}{3}\right)^{x}\right) 
5
55 
= 5.0
      /     -x\
 lim  \2 + 3  /
x->-1-
lim⁡x→−1−(2+(13)x)\lim_{x \to -1^-}\left(2 + \left(\frac{1}{3}\right)^{x}\right) 
5
55 
= 5.0
= 5.0
Other limits x→0, -oo, +oo, 1
lim⁡x→−1−(2+(13)x)=5\lim_{x \to -1^-}\left(2 + \left(\frac{1}{3}\right)^{x}\right) = 5
More at x→-1 from the left
lim⁡x→−1+(2+(13)x)=5\lim_{x \to -1^+}\left(2 + \left(\frac{1}{3}\right)^{x}\right) = 5
lim⁡x→∞(2+(13)x)=2\lim_{x \to \infty}\left(2 + \left(\frac{1}{3}\right)^{x}\right) = 2
More at x→oo
lim⁡x→0−(2+(13)x)=3\lim_{x \to 0^-}\left(2 + \left(\frac{1}{3}\right)^{x}\right) = 3
More at x→0 from the left
lim⁡x→0+(2+(13)x)=3\lim_{x \to 0^+}\left(2 + \left(\frac{1}{3}\right)^{x}\right) = 3
More at x→0 from the right
lim⁡x→1−(2+(13)x)=73\lim_{x \to 1^-}\left(2 + \left(\frac{1}{3}\right)^{x}\right) = \frac{7}{3}
More at x→1 from the left
lim⁡x→1+(2+(13)x)=73\lim_{x \to 1^+}\left(2 + \left(\frac{1}{3}\right)^{x}\right) = \frac{7}{3}
More at x→1 from the right
lim⁡x→−∞(2+(13)x)=∞\lim_{x \to -\infty}\left(2 + \left(\frac{1}{3}\right)^{x}\right) = \infty
More at x→-oo
Numerical answer [src] 
5.0
5.0
The graph
Limit of the function 2+(1/3)^x
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