Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 7^(1/(-3+x))
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Limit of (3-3*x^2+4*x^4+6*x^3)/(2*x^2+7*x^4)
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Limit of ((5+4*x)/(-1+5*x))^(1+3*x)
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Limit of (-6-x^2-3*x+4*x^3)/(3-x^2+2*x^3)
- Integral of d{x}:
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x*sinh(x)
- Graphing y =:
- x*sinh(x)
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Identical expressions
- x*sinh(x)
- x multiply by hyperbolic sinus of e of (x)
- xsinh(x)
- xsinhx
Limit of the function x*sinh(x)
The solution
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lim (x*sinh(x)) x->oo
$$\lim_{x \to \infty}\left(x \sinh{\left(x \right)}\right)$$
Limit(x*sinh(x), x, oo, dir='-')
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
$$\lim_{x \to \infty}\left(x \sinh{\left(x \right)}\right) = \infty$$
$$\lim_{x \to 0^-}\left(x \sinh{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \sinh{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \sinh{\left(x \right)}\right) = \frac{-1 + e^{2}}{2 e}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \sinh{\left(x \right)}\right) = \frac{-1 + e^{2}}{2 e}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \sinh{\left(x \right)}\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x \sinh{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \sinh{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \sinh{\left(x \right)}\right) = \frac{-1 + e^{2}}{2 e}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \sinh{\left(x \right)}\right) = \frac{-1 + e^{2}}{2 e}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \sinh{\left(x \right)}\right) = \infty$$
More at x→-oo
The graph