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

Limit of the function e^x*log(x)

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     / x       \
 lim \E *log(x)/
x->0+
$$\lim_{x \to 0^+}\left(e^{x} \log{\left(x \right)}\right)$$ 
Limit(E^x*log(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
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Rapid solution [src] 
-oo
$$-\infty$$
Expand and simplify
One‐sided limits [src] 
     / x       \
 lim \E *log(x)/
x->0+
$$\lim_{x \to 0^+}\left(e^{x} \log{\left(x \right)}\right)$$ 
-oo
$$-\infty$$ 
= -5.05061712212235
     / x       \
 lim \E *log(x)/
x->0-
$$\lim_{x \to 0^-}\left(e^{x} \log{\left(x \right)}\right)$$ 
-oo
$$-\infty$$ 
= (-8.85777307925138 + 3.12351848844892j)
= (-8.85777307925138 + 3.12351848844892j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(e^{x} \log{\left(x \right)}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(e^{x} \log{\left(x \right)}\right) = -\infty$$
$$\lim_{x \to \infty}\left(e^{x} \log{\left(x \right)}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(e^{x} \log{\left(x \right)}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(e^{x} \log{\left(x \right)}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(e^{x} \log{\left(x \right)}\right) = 0$$
More at x→-oo
Numerical answer [src] 
-5.05061712212235
-5.05061712212235
The graph
Limit of the function e^x*log(x)
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