Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of cos(sqrt(x))
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Limit of sqrt(x)*log(x)
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Limit of cos(x)*log(x)
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Limit of sin(z)
- Derivative of:
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cos(sqrt(x))
- Integral of d{x}:
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cos(sqrt(x))
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Identical expressions
- cos(sqrt(x))
- co sinus of e of ( square root of (x))
- cos(√(x))
- cossqrtx
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Similar expressions
- acos(sqrt(x+x^2)-x)
Limit of the function cos(sqrt(x))
The solution
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/ ___\ lim cos\\/ x / x->oo
$$\lim_{x \to \infty} \cos{\left(\sqrt{x} \right)}$$
Limit(cos(sqrt(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
$$\lim_{x \to \infty} \cos{\left(\sqrt{x} \right)} = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to 0^-} \cos{\left(\sqrt{x} \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(\sqrt{x} \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(\sqrt{x} \right)} = \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(\sqrt{x} \right)} = \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(\sqrt{x} \right)} = \infty$$
More at x→-oo
$$\lim_{x \to 0^-} \cos{\left(\sqrt{x} \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(\sqrt{x} \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(\sqrt{x} \right)} = \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(\sqrt{x} \right)} = \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(\sqrt{x} \right)} = \infty$$
More at x→-oo
The graph