Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of -2+x^3+6*x
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Limit of ((-2+x)/x)^(2*x)
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Limit of (2+x^2-3*x)/(4+x^2-5*x)
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Limit of ((1+x)/(3+x))^(1+2*x)
- Integral of d{x}:
- cos(sin(x))
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Identical expressions
- cos(sin(x))
- co sinus of e of ( sinus of (x))
- cossinx
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Similar expressions
- pi*acos(sin(x)/x)/x
- cos(sinx)
Limit of the function cos(sin(x))
The solution
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lim cos(sin(x)) x->oo
$$\lim_{x \to \infty} \cos{\left(\sin{\left(x \right)} \right)}$$
Limit(cos(sin(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
$$\lim_{x \to \infty} \cos{\left(\sin{\left(x \right)} \right)} = \left\langle \cos{\left(1 \right)}, 1\right\rangle$$
$$\lim_{x \to 0^-} \cos{\left(\sin{\left(x \right)} \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(\sin{\left(x \right)} \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(\sin{\left(x \right)} \right)} = \cos{\left(\sin{\left(1 \right)} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(\sin{\left(x \right)} \right)} = \cos{\left(\sin{\left(1 \right)} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(\sin{\left(x \right)} \right)} = \left\langle \cos{\left(1 \right)}, 1\right\rangle$$
More at x→-oo
$$\lim_{x \to 0^-} \cos{\left(\sin{\left(x \right)} \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(\sin{\left(x \right)} \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(\sin{\left(x \right)} \right)} = \cos{\left(\sin{\left(1 \right)} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(\sin{\left(x \right)} \right)} = \cos{\left(\sin{\left(1 \right)} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(\sin{\left(x \right)} \right)} = \left\langle \cos{\left(1 \right)}, 1\right\rangle$$
More at x→-oo
The graph