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(1-log(7*x))^(7*x)

Limit of the function (1-log(7*x))^(7*x)

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                   7*x
 lim (1 - log(7*x))   
x->0+                 
limx0+(1log(7x))7x\lim_{x \to 0^+} \left(1 - \log{\left(7 x \right)}\right)^{7 x}
Limit((1 - log(7*x))^(7*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
02468-8-6-4-2-1010010e35
Rapid solution [src]
1
11
Other limits x→0, -oo, +oo, 1
limx0(1log(7x))7x=1\lim_{x \to 0^-} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = 1
More at x→0 from the left
limx0+(1log(7x))7x=1\lim_{x \to 0^+} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = 1
limx(1log(7x))7x=0\lim_{x \to \infty} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = 0
More at x→oo
limx1(1log(7x))7x=21log(7)535log(7)3log(7)77log(7)+1+21log(7)2+7log(7)6+35log(7)4\lim_{x \to 1^-} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = - 21 \log{\left(7 \right)}^{5} - 35 \log{\left(7 \right)}^{3} - \log{\left(7 \right)}^{7} - 7 \log{\left(7 \right)} + 1 + 21 \log{\left(7 \right)}^{2} + 7 \log{\left(7 \right)}^{6} + 35 \log{\left(7 \right)}^{4}
More at x→1 from the left
limx1+(1log(7x))7x=21log(7)535log(7)3log(7)77log(7)+1+21log(7)2+7log(7)6+35log(7)4\lim_{x \to 1^+} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = - 21 \log{\left(7 \right)}^{5} - 35 \log{\left(7 \right)}^{3} - \log{\left(7 \right)}^{7} - 7 \log{\left(7 \right)} + 1 + 21 \log{\left(7 \right)}^{2} + 7 \log{\left(7 \right)}^{6} + 35 \log{\left(7 \right)}^{4}
More at x→1 from the right
limx(1log(7x))7x=0\lim_{x \to -\infty} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = 0
More at x→-oo
One‐sided limits [src]
                   7*x
 lim (1 - log(7*x))   
x->0+                 
limx0+(1log(7x))7x\lim_{x \to 0^+} \left(1 - \log{\left(7 x \right)}\right)^{7 x}
1
11
= (1.00335674408759 - 9.38301555323147e-6j)
                   7*x
 lim (1 - log(7*x))   
x->0-                 
limx0(1log(7x))7x\lim_{x \to 0^-} \left(1 - \log{\left(7 x \right)}\right)^{7 x}
1
11
= (0.996595785860645 + 0.000625569892627682j)
= (0.996595785860645 + 0.000625569892627682j)
Numerical answer [src]
(1.00335674408759 - 9.38301555323147e-6j)
(1.00335674408759 - 9.38301555323147e-6j)
The graph
Limit of the function (1-log(7*x))^(7*x)