Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-2*x^2+4*x^3+5*x)/(3*x^2+7*x)
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Limit of (-cos(5*x)+cos(3*x))/x^2
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Limit of (-1+cos(7*x))/(-1+cos(3*x))
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Limit of (16+x^2+10*x)/(-6+x^2-x)
- Graphing y =:
- cos(x)*cos(2*x)
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Identical expressions
- cos(x)*cos(two *x)
- co sinus of e of (x) multiply by co sinus of e of (2 multiply by x)
- co sinus of e of (x) multiply by co sinus of e of (two multiply by x)
- cos(x)cos(2x)
- cosxcos2x
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Similar expressions
- cosx*cos(2*x)
Limit of the function cos(x)*cos(2*x)
The solution
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lim (cos(x)*cos(2*x)) x->oo
$$\lim_{x \to \infty}\left(\cos{\left(x \right)} \cos{\left(2 x \right)}\right)$$
Limit(cos(x)*cos(2*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
$$\lim_{x \to \infty}\left(\cos{\left(x \right)} \cos{\left(2 x \right)}\right) = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to 0^-}\left(\cos{\left(x \right)} \cos{\left(2 x \right)}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\cos{\left(x \right)} \cos{\left(2 x \right)}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\cos{\left(x \right)} \cos{\left(2 x \right)}\right) = \cos{\left(1 \right)} \cos{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\cos{\left(x \right)} \cos{\left(2 x \right)}\right) = \cos{\left(1 \right)} \cos{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\cos{\left(x \right)} \cos{\left(2 x \right)}\right) = \left\langle -1, 1\right\rangle$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\cos{\left(x \right)} \cos{\left(2 x \right)}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\cos{\left(x \right)} \cos{\left(2 x \right)}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\cos{\left(x \right)} \cos{\left(2 x \right)}\right) = \cos{\left(1 \right)} \cos{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\cos{\left(x \right)} \cos{\left(2 x \right)}\right) = \cos{\left(1 \right)} \cos{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\cos{\left(x \right)} \cos{\left(2 x \right)}\right) = \left\langle -1, 1\right\rangle$$
More at x→-oo
The graph