Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-exp(-x)+exp(x))/(exp(x)+exp(-x))
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Limit of ((3+5*x)/(-2+4*x))^(1+3*x)
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Limit of (3+3*x^3+5*x+5*x^2)/(-1+x^2)
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Limit of (3-x^2+5*x)/(4*x^7+81*x)
- Derivative of:
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x*cos(2*x)
- Integral of d{x}:
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x*cos(2*x)
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Identical expressions
- x*cos(two *x)
- x multiply by co sinus of e of (2 multiply by x)
- x multiply by co sinus of e of (two multiply by x)
- xcos(2x)
- xcos2x
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Similar expressions
- (1-cos(x)*cos(2*x)*cos(3*x))/(1-cos(x))
- atan(8*x)*cos(2*x)/sin(4*x)
Limit of the function x*cos(2*x)
The solution
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lim (x*cos(2*x)) x->-oo
$$\lim_{x \to -\infty}\left(x \cos{\left(2 x \right)}\right)$$
Limit(x*cos(2*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
$$\lim_{x \to -\infty}\left(x \cos{\left(2 x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to \infty}\left(x \cos{\left(2 x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-}\left(x \cos{\left(2 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \cos{\left(2 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \cos{\left(2 x \right)}\right) = \cos{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \cos{\left(2 x \right)}\right) = \cos{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to \infty}\left(x \cos{\left(2 x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-}\left(x \cos{\left(2 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \cos{\left(2 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \cos{\left(2 x \right)}\right) = \cos{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \cos{\left(2 x \right)}\right) = \cos{\left(2 \right)}$$
More at x→1 from the right
The graph