Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of (1-3*x^2+2*x^3)/(x^3+2*x+4*x^2)
-
Limit of (-4-7*x+2*x^2)/(4-13*x+3*x^2)
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Limit of 5+3*n
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Limit of (-12+x^2-4*x)/(48+x^2-14*x)
- Graphing y =:
- 2*cos(2*x)
- Integral of d{x}:
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2*cos(2*x)
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Identical expressions
- two *cos(two *x)
- 2 multiply by co sinus of e of (2 multiply by x)
- two multiply by co sinus of e of (two multiply by x)
- 2cos(2x)
- 2cos2x
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Similar expressions
- log(1+4*asin(x^2))/(atan(x^2)*cos(2*x))
Limit of the function 2*cos(2*x)
The solution
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[src]
lim (2*cos(2*x))
-pi
x->----+
12
$$\lim_{x \to \frac{\left(-1\right) \pi}{12}^+}\left(2 \cos{\left(2 x \right)}\right)$$
Limit(2*cos(2*x), x, (-pi)/12)
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
One‐sided limits
[src]
lim (2*cos(2*x))
-pi
x->----+
12
$$\lim_{x \to \frac{\left(-1\right) \pi}{12}^+}\left(2 \cos{\left(2 x \right)}\right)$$
___ \/ 3
$$\sqrt{3}$$
= 1.73205080756888
lim (2*cos(2*x))
-pi
x->-----
12
$$\lim_{x \to \frac{\left(-1\right) \pi}{12}^-}\left(2 \cos{\left(2 x \right)}\right)$$
___ \/ 3
$$\sqrt{3}$$
= 1.73205080756888
= 1.73205080756888
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{\left(-1\right) \pi}{12}^-}\left(2 \cos{\left(2 x \right)}\right) = \sqrt{3}$$
More at x→(-pi)/12 from the left
$$\lim_{x \to \frac{\left(-1\right) \pi}{12}^+}\left(2 \cos{\left(2 x \right)}\right) = \sqrt{3}$$
$$\lim_{x \to \infty}\left(2 \cos{\left(2 x \right)}\right) = \left\langle -2, 2\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-}\left(2 \cos{\left(2 x \right)}\right) = 2$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(2 \cos{\left(2 x \right)}\right) = 2$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(2 \cos{\left(2 x \right)}\right) = 2 \cos{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(2 \cos{\left(2 x \right)}\right) = 2 \cos{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(2 \cos{\left(2 x \right)}\right) = \left\langle -2, 2\right\rangle$$
More at x→-oo
More at x→(-pi)/12 from the left
$$\lim_{x \to \frac{\left(-1\right) \pi}{12}^+}\left(2 \cos{\left(2 x \right)}\right) = \sqrt{3}$$
$$\lim_{x \to \infty}\left(2 \cos{\left(2 x \right)}\right) = \left\langle -2, 2\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-}\left(2 \cos{\left(2 x \right)}\right) = 2$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(2 \cos{\left(2 x \right)}\right) = 2$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(2 \cos{\left(2 x \right)}\right) = 2 \cos{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(2 \cos{\left(2 x \right)}\right) = 2 \cos{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(2 \cos{\left(2 x \right)}\right) = \left\langle -2, 2\right\rangle$$
More at x→-oo
The graph