Mister Exam
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How to use it?
- Limit of the function:
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Limit of 2^(-n)*2^(1+n)
- Limit of tan(k*x)/x
-
Limit of (-x+tan(x))/(x+2*sin(x))
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Limit of asin(5*x)/tan(3*x)
- Derivative of:
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x-sin(x)
- Graphing y =:
- x-sin(x)
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Identical expressions
- x-sin(x)
- x minus sinus of (x)
- x-sinx
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Similar expressions
- x+sin(x)
- x-sinx
Limit of the function x-sin(x)
The solution
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lim (x - sin(x)) x->oo
$$\lim_{x \to \infty}\left(x - \sin{\left(x \right)}\right)$$
Limit(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
$$\lim_{x \to \infty}\left(x - \sin{\left(x \right)}\right) = \infty$$
$$\lim_{x \to 0^-}\left(x - \sin{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x - \sin{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x - \sin{\left(x \right)}\right) = 1 - \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x - \sin{\left(x \right)}\right) = 1 - \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x - \sin{\left(x \right)}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x - \sin{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x - \sin{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x - \sin{\left(x \right)}\right) = 1 - \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x - \sin{\left(x \right)}\right) = 1 - \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x - \sin{\left(x \right)}\right) = -\infty$$
More at x→-oo
The graph