Mister Exam
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- Limit of the function:
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Limit of sign(x)
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Limit of -sinh(x)+cosh(x)
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Limit of 3+3*n^2+5*n-32*n^3/5
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Limit of x/sin(x)
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Identical expressions
- -sinh(x)+cosh(x)
- minus hyperbolic sinus of e of (x) plus hyperbolic co sinus of e of ine of (x)
- -sinhx+coshx
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Similar expressions
- sinh(x)+cosh(x)
- -sinh(x)-cosh(x)
Limit of the function -sinh(x)+cosh(x)
The solution
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lim (-sinh(x) + cosh(x)) x->oo
$$\lim_{x \to \infty}\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)}\right)$$
Limit(-sinh(x) + cosh(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
$$\lim_{x \to \infty}\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) = 0$$
$$\lim_{x \to 0^-}\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) = - \sinh{\left(1 \right)} + \cosh{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) = - \sinh{\left(1 \right)} + \cosh{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) = - \sinh{\left(1 \right)} + \cosh{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) = - \sinh{\left(1 \right)} + \cosh{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- \sinh{\left(x \right)} + \cosh{\left(x \right)}\right) = \infty$$
More at x→-oo
The graph