Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-1+e^(2*x))/(3*x)
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Limit of (-1+3*x)/(5+x^2+7*x)
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Limit of 1+13*x/5
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Limit of (7+x+x^2)/(-1+e^x)
- Graphing y =:
- atan(x)/3
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Identical expressions
- atan(x)/ three
- arc tangent of gent of (x) divide by 3
- arc tangent of gent of (x) divide by three
- atanx/3
- atan(x) divide by 3
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Similar expressions
- atan(x/3)/3
- x*atan(x/3)
- 4*x+atan(x/3)
- (1-x/6+atan(x/3))/x
- atan(x)/(3*x)
- arctan(x)/3
- arctanx/3
Limit of the function atan(x)/3
The solution
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/atan(x)\ lim |-------| x->oo\ 3 /
$$\lim_{x \to \infty}\left(\frac{\operatorname{atan}{\left(x \right)}}{3}\right)$$
Limit(atan(x)/3, 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
$$\lim_{x \to \infty}\left(\frac{\operatorname{atan}{\left(x \right)}}{3}\right) = \frac{\pi}{6}$$
$$\lim_{x \to 0^-}\left(\frac{\operatorname{atan}{\left(x \right)}}{3}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\operatorname{atan}{\left(x \right)}}{3}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\operatorname{atan}{\left(x \right)}}{3}\right) = \frac{\pi}{12}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\operatorname{atan}{\left(x \right)}}{3}\right) = \frac{\pi}{12}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\operatorname{atan}{\left(x \right)}}{3}\right) = - \frac{\pi}{6}$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{\operatorname{atan}{\left(x \right)}}{3}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\operatorname{atan}{\left(x \right)}}{3}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\operatorname{atan}{\left(x \right)}}{3}\right) = \frac{\pi}{12}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\operatorname{atan}{\left(x \right)}}{3}\right) = \frac{\pi}{12}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\operatorname{atan}{\left(x \right)}}{3}\right) = - \frac{\pi}{6}$$
More at x→-oo
The graph