Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of ((-2+x)/x)^(2*x)
-
Limit of (-1+tan(x)^(1/3))/(-1+log(x)/log(pi/4))
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Limit of (-5+sqrt(9+x^2))/(-3+sqrt(5+x))
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Limit of sin(7*x)/tan(4*x)
- Integral of d{x}:
- cos(pi/(6*x))
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Identical expressions
- cos(pi/(six *x))
- co sinus of e of ( Pi divide by (6 multiply by x))
- co sinus of e of ( Pi divide by (six multiply by x))
- cos(pi/(6x))
- cospi/6x
- cos(pi divide by (6*x))
Limit of the function cos(pi/(6*x))
The solution
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/ pi\ lim cos|---| x->oo \6*x/
$$\lim_{x \to \infty} \cos{\left(\frac{\pi}{6 x} \right)}$$
Limit(cos(pi/((6*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
$$\lim_{x \to \infty} \cos{\left(\frac{\pi}{6 x} \right)} = 1$$
$$\lim_{x \to 0^-} \cos{\left(\frac{\pi}{6 x} \right)} = \left\langle -1, 1\right\rangle$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(\frac{\pi}{6 x} \right)} = \left\langle -1, 1\right\rangle$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(\frac{\pi}{6 x} \right)} = \frac{\sqrt{3}}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(\frac{\pi}{6 x} \right)} = \frac{\sqrt{3}}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(\frac{\pi}{6 x} \right)} = 1$$
More at x→-oo
$$\lim_{x \to 0^-} \cos{\left(\frac{\pi}{6 x} \right)} = \left\langle -1, 1\right\rangle$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(\frac{\pi}{6 x} \right)} = \left\langle -1, 1\right\rangle$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(\frac{\pi}{6 x} \right)} = \frac{\sqrt{3}}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(\frac{\pi}{6 x} \right)} = \frac{\sqrt{3}}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(\frac{\pi}{6 x} \right)} = 1$$
More at x→-oo
The graph