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Limit of the function log(-1+x)/cot(pi*x)


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The solution

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     /log(-1 + x)\
 lim |-----------|
x->oo\ cot(pi*x) /
$$\lim_{x \to \infty}\left(\frac{\log{\left(x - 1 \right)}}{\cot{\left(\pi x \right)}}\right)$$
Limit(log(-1 + x)/cot(pi*x), x, oo, dir='-')
The graph
Rapid solution [src]
     /log(-1 + x)\
 lim |-----------|
x->oo\ cot(pi*x) /
$$\lim_{x \to \infty}\left(\frac{\log{\left(x - 1 \right)}}{\cot{\left(\pi x \right)}}\right)$$
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{\log{\left(x - 1 \right)}}{\cot{\left(\pi x \right)}}\right)$$
$$\lim_{x \to 0^-}\left(\frac{\log{\left(x - 1 \right)}}{\cot{\left(\pi x \right)}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x - 1 \right)}}{\cot{\left(\pi x \right)}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\log{\left(x - 1 \right)}}{\cot{\left(\pi x \right)}}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\log{\left(x - 1 \right)}}{\cot{\left(\pi x \right)}}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\log{\left(x - 1 \right)}}{\cot{\left(\pi x \right)}}\right)$$
More at x→-oo
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 above examples also contain:

    • the modulus or absolute value: absolute(x) or |x|
    • square roots sqrt(x),
      cubic roots cbrt(x)
    • trigonometric functions:
      sinus sin(x), cosine cos(x), tangent tan(x), cotangent ctan(x)
    • exponential functions and exponents exp(x)
    • inverse trigonometric functions:
      arcsine asin(x), arccosine acos(x), arctangent atan(x), arccotangent acot(x)
    • natural logarithms ln(x),
      decimal logarithms log(x)
    • hyperbolic functions:
      hyperbolic sine sh(x), hyperbolic cosine ch(x), hyperbolic tangent and cotangent tanh(x), ctanh(x)
    • inverse hyperbolic functions:
      hyperbolic arcsine asinh(x), hyperbolic arccosinus acosh(x), hyperbolic arctangent atanh(x), hyperbolic arccotangent acoth(x)
    • other trigonometry and hyperbolic functions:
      secant sec(x), cosecant csc(x), arcsecant asec(x), arccosecant acsc(x), hyperbolic secant sech(x), hyperbolic cosecant csch(x), hyperbolic arcsecant asech(x), hyperbolic arccosecant acsch(x)
    • rounding functions:
      round down floor(x), round up ceiling(x)
    • the sign of a number:
    • for probability theory:
      the error function erf(x) (integral of probability), Laplace function laplace(x)
    • Factorial of x:
      x! or factorial(x)
    • Gamma function gamma(x)
    • Lambert's function LambertW(x)

    The insertion rules

    The following operations can be performed

    - multiplication
    - division
    - squaring
    - cubing
    - raising to the power
    x + 7
    - addition
    x - 6
    - subtraction
    Real numbers
    insert as 7.5, no 7,5


    - number Pi
    - the base of natural logarithm
    - complex number
    - symbol of infinity
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