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7^(1/(-3+x))
Limit of the function/ 7^(1/(-3+x))

Limit of the function 7^(1/(-3+x))

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The solution

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        1   
      ------
      -3 + x
 lim 7      
x->3+
$$\lim_{x \to 3^+} 7^{\frac{1}{x - 3}}$$ 
Limit(7^(1/(-3 + x)), x, 3)
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 3^-} 7^{\frac{1}{x - 3}} = \infty$$
More at x→3 from the left
$$\lim_{x \to 3^+} 7^{\frac{1}{x - 3}} = \infty$$
$$\lim_{x \to \infty} 7^{\frac{1}{x - 3}} = 1$$
More at x→oo
$$\lim_{x \to 0^-} 7^{\frac{1}{x - 3}} = \frac{7^{\frac{2}{3}}}{7}$$
More at x→0 from the left
$$\lim_{x \to 0^+} 7^{\frac{1}{x - 3}} = \frac{7^{\frac{2}{3}}}{7}$$
More at x→0 from the right
$$\lim_{x \to 1^-} 7^{\frac{1}{x - 3}} = \frac{\sqrt{7}}{7}$$
More at x→1 from the left
$$\lim_{x \to 1^+} 7^{\frac{1}{x - 3}} = \frac{\sqrt{7}}{7}$$
More at x→1 from the right
$$\lim_{x \to -\infty} 7^{\frac{1}{x - 3}} = 1$$
More at x→-oo
Rapid solution [src] 
oo
$$\infty$$
Expand and simplify
One‐sided limits [src] 
        1   
      ------
      -3 + x
 lim 7      
x->3+
$$\lim_{x \to 3^+} 7^{\frac{1}{x - 3}}$$ 
oo
$$\infty$$ 
= 3.96949676453093e-72
        1   
      ------
      -3 + x
 lim 7      
x->3-
$$\lim_{x \to 3^-} 7^{\frac{1}{x - 3}}$$ 
0
$$0$$ 
= -4.44589751028753e-82
= -4.44589751028753e-82
Numerical answer [src] 
3.96949676453093e-72
3.96949676453093e-72
The graph
Limit of the function 7^(1/(-3+x))
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