Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+3*x)^(5/x)
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Limit of x^2/(-2+sqrt(4+x^2))
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Limit of ((5+x^2-6*x)/(5+x^2-5*x))^(2+3*x)
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Limit of (2+x^2+3*x)/(-4+x^2)
- Derivative of:
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atan(3*x)
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Identical expressions
- atan(three *x)
- arc tangent of gent of (3 multiply by x)
- arc tangent of gent of (three multiply by x)
- atan(3x)
- atan3x
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Similar expressions
- arctan(3*x)
Limit of the function atan(3*x)
The solution
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lim atan(3*x) x->-oo
$$\lim_{x \to -\infty} \operatorname{atan}{\left(3 x \right)}$$
Limit(atan(3*x), x, -oo)
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
$$\lim_{x \to -\infty} \operatorname{atan}{\left(3 x \right)} = - \frac{\pi}{2}$$
$$\lim_{x \to \infty} \operatorname{atan}{\left(3 x \right)} = \frac{\pi}{2}$$
More at x→oo
$$\lim_{x \to 0^-} \operatorname{atan}{\left(3 x \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{atan}{\left(3 x \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \operatorname{atan}{\left(3 x \right)} = \operatorname{atan}{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{atan}{\left(3 x \right)} = \operatorname{atan}{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to \infty} \operatorname{atan}{\left(3 x \right)} = \frac{\pi}{2}$$
More at x→oo
$$\lim_{x \to 0^-} \operatorname{atan}{\left(3 x \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \operatorname{atan}{\left(3 x \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \operatorname{atan}{\left(3 x \right)} = \operatorname{atan}{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \operatorname{atan}{\left(3 x \right)} = \operatorname{atan}{\left(3 \right)}$$
More at x→1 from the right
The graph