Mister Exam
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How to use it?
- Limit of the function:
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Limit of (1-log(7*x))^(7*x)
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Limit of sin(x)/sqrt(1-cos(x))
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Limit of (e^x-e^2)/(-2+x)
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Limit of tan(3*x)/(7*x)
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Identical expressions
- (one -log(seven *x))^(seven *x)
- (1 minus logarithm of (7 multiply by x)) to the power of (7 multiply by x)
- (one minus logarithm of (seven multiply by x)) to the power of (seven multiply by x)
- (1-log(7*x))(7*x)
- 1-log7*x7*x
- (1-log(7x))^(7x)
- (1-log(7x))(7x)
- 1-log7x7x
- 1-log7x^7x
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Similar expressions
- (1+log(7*x))^(7*x)
Limit of the function (1-log(7*x))^(7*x)
The solution
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[src]
7*x lim (1 - log(7*x)) x->0+
$$\lim_{x \to 0^+} \left(1 - \log{\left(7 x \right)}\right)^{7 x}$$
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = 1$$
$$\lim_{x \to \infty} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = 0$$
More at x→oo
$$\lim_{x \to 1^-} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = - 21 \log{\left(7 \right)}^{5} - 35 \log{\left(7 \right)}^{3} - \log{\left(7 \right)}^{7} - 7 \log{\left(7 \right)} + 1 + 21 \log{\left(7 \right)}^{2} + 7 \log{\left(7 \right)}^{6} + 35 \log{\left(7 \right)}^{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = - 21 \log{\left(7 \right)}^{5} - 35 \log{\left(7 \right)}^{3} - \log{\left(7 \right)}^{7} - 7 \log{\left(7 \right)} + 1 + 21 \log{\left(7 \right)}^{2} + 7 \log{\left(7 \right)}^{6} + 35 \log{\left(7 \right)}^{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = 1$$
$$\lim_{x \to \infty} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = 0$$
More at x→oo
$$\lim_{x \to 1^-} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = - 21 \log{\left(7 \right)}^{5} - 35 \log{\left(7 \right)}^{3} - \log{\left(7 \right)}^{7} - 7 \log{\left(7 \right)} + 1 + 21 \log{\left(7 \right)}^{2} + 7 \log{\left(7 \right)}^{6} + 35 \log{\left(7 \right)}^{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = - 21 \log{\left(7 \right)}^{5} - 35 \log{\left(7 \right)}^{3} - \log{\left(7 \right)}^{7} - 7 \log{\left(7 \right)} + 1 + 21 \log{\left(7 \right)}^{2} + 7 \log{\left(7 \right)}^{6} + 35 \log{\left(7 \right)}^{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(1 - \log{\left(7 x \right)}\right)^{7 x} = 0$$
More at x→-oo
One‐sided limits
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7*x lim (1 - log(7*x)) x->0+
$$\lim_{x \to 0^+} \left(1 - \log{\left(7 x \right)}\right)^{7 x}$$
1
$$1$$
= (1.00335674408759 - 9.38301555323147e-6j)
7*x lim (1 - log(7*x)) x->0-
$$\lim_{x \to 0^-} \left(1 - \log{\left(7 x \right)}\right)^{7 x}$$
1
$$1$$
= (0.996595785860645 + 0.000625569892627682j)
= (0.996595785860645 + 0.000625569892627682j)
Numerical answer
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(1.00335674408759 - 9.38301555323147e-6j)
(1.00335674408759 - 9.38301555323147e-6j)
The graph