Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 1-cos(3*x)
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Limit of ((6+5*x)/(-1+5*x))^((1+2*x^2)/x)
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Limit of (-3*5^(1+x)+5*2^x)/(2*5^x+100*2^x)
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Limit of (4^x-9^x)/(4^(1+x)+9^(1+x))
- Derivative of:
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atan(t)
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Identical expressions
- atan(t)
- arc tangent of gent of (t)
- atant
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Similar expressions
- atan(tan(x))
- arctan(t)
Limit of the function atan(t)
The solution
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lim atan(t) t->oo
$$\lim_{t \to \infty} \operatorname{atan}{\left(t \right)}$$
Limit(atan(t), t, 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 t→0, -oo, +oo, 1
$$\lim_{t \to \infty} \operatorname{atan}{\left(t \right)} = \frac{\pi}{2}$$
$$\lim_{t \to 0^-} \operatorname{atan}{\left(t \right)} = 0$$
More at t→0 from the left
$$\lim_{t \to 0^+} \operatorname{atan}{\left(t \right)} = 0$$
More at t→0 from the right
$$\lim_{t \to 1^-} \operatorname{atan}{\left(t \right)} = \frac{\pi}{4}$$
More at t→1 from the left
$$\lim_{t \to 1^+} \operatorname{atan}{\left(t \right)} = \frac{\pi}{4}$$
More at t→1 from the right
$$\lim_{t \to -\infty} \operatorname{atan}{\left(t \right)} = - \frac{\pi}{2}$$
More at t→-oo
$$\lim_{t \to 0^-} \operatorname{atan}{\left(t \right)} = 0$$
More at t→0 from the left
$$\lim_{t \to 0^+} \operatorname{atan}{\left(t \right)} = 0$$
More at t→0 from the right
$$\lim_{t \to 1^-} \operatorname{atan}{\left(t \right)} = \frac{\pi}{4}$$
More at t→1 from the left
$$\lim_{t \to 1^+} \operatorname{atan}{\left(t \right)} = \frac{\pi}{4}$$
More at t→1 from the right
$$\lim_{t \to -\infty} \operatorname{atan}{\left(t \right)} = - \frac{\pi}{2}$$
More at t→-oo
The graph