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e^(3*x)
Limit of the function/ e^(3*x)

Limit of the function e^(3*x)

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The solution

You have entered [src] 
      3*x
 lim E   
x->0+
lim⁡x→0+e3x\lim_{x \to 0^+} e^{3 x} 
Limit(E^(3*x), x, 0)
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
02468-8-6-4-2-1010020000000000000
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Rapid solution [src] 
1
11
Expand and simplify
One‐sided limits [src] 
      3*x
 lim E   
x->0+
lim⁡x→0+e3x\lim_{x \to 0^+} e^{3 x} 
1
11 
= 1.0
      3*x
 lim E   
x->0-
lim⁡x→0−e3x\lim_{x \to 0^-} e^{3 x} 
1
11 
= 1.0
= 1.0
Other limits x→0, -oo, +oo, 1
lim⁡x→0−e3x=1\lim_{x \to 0^-} e^{3 x} = 1
More at x→0 from the left
lim⁡x→0+e3x=1\lim_{x \to 0^+} e^{3 x} = 1
lim⁡x→∞e3x=∞\lim_{x \to \infty} e^{3 x} = \infty
More at x→oo
lim⁡x→1−e3x=e3\lim_{x \to 1^-} e^{3 x} = e^{3}
More at x→1 from the left
lim⁡x→1+e3x=e3\lim_{x \to 1^+} e^{3 x} = e^{3}
More at x→1 from the right
lim⁡x→−∞e3x=0\lim_{x \to -\infty} e^{3 x} = 0
More at x→-oo
Numerical answer [src] 
1.0
1.0
The graph
Limit of the function e^(3*x)
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