Mister Exam
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How to use it?
- Limit of the function:
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Limit of (-sin(sin(x))+tan(tan(x)))/(-sin(x)+tan(x))
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Limit of sin(x)/(x^2-pi^2)^2
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Limit of (-log(1+x^2)+sin(x))/(2-e^(3*x)-sqrt(1+x))
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Limit of -sin(6*x)/(2*x)
- Derivative of:
- -x*cos(x)+sin(x)
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Identical expressions
- -x*cos(x)+sin(x)
- minus x multiply by co sinus of e of (x) plus sinus of (x)
- -xcos(x)+sin(x)
- -xcosx+sinx
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Similar expressions
- x*cos(x)+sin(x)
- -x*cos(x)-sin(x)
- -x*cosx+sinx
Limit of the function -x*cos(x)+sin(x)
The solution
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lim (-x*cos(x) + sin(x)) x->oo
$$\lim_{x \to \infty}\left(- x \cos{\left(x \right)} + \sin{\left(x \right)}\right)$$
Limit((-x)*cos(x) + sin(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
$$\lim_{x \to \infty}\left(- x \cos{\left(x \right)} + \sin{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to 0^-}\left(- x \cos{\left(x \right)} + \sin{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x \cos{\left(x \right)} + \sin{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x \cos{\left(x \right)} + \sin{\left(x \right)}\right) = - \cos{\left(1 \right)} + \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x \cos{\left(x \right)} + \sin{\left(x \right)}\right) = - \cos{\left(1 \right)} + \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x \cos{\left(x \right)} + \sin{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- x \cos{\left(x \right)} + \sin{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x \cos{\left(x \right)} + \sin{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x \cos{\left(x \right)} + \sin{\left(x \right)}\right) = - \cos{\left(1 \right)} + \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x \cos{\left(x \right)} + \sin{\left(x \right)}\right) = - \cos{\left(1 \right)} + \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x \cos{\left(x \right)} + \sin{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
The graph