Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (3-3*x^2+4*x^4+6*x^3)/(2*x^2+7*x^4)
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Limit of ((5+4*x)/(-1+5*x))^(1+3*x)
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Limit of (1+x^3-2*x)/(8+x^10-9*x)
- Limit of x^2+a/(x^3-a^3)-x*(1+a)
- Integral of d{x}:
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1/(2+cos(x))
- Derivative of:
- 1/(2+cos(x))
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Identical expressions
- one /(two +cos(x))
- 1 divide by (2 plus co sinus of e of (x))
- one divide by (two plus co sinus of e of (x))
- 1/2+cosx
- 1 divide by (2+cos(x))
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Similar expressions
- -(-1/2+cos(x))/cos(x+pi/6)
- 1/(2-cos(x))
- (x-pi/3)/(-1/2+cos(x))
- (x-2*pi)^2/log(1/2+cos(x)/2)
- (x-pi/3-2*pi*k)^3/(-1/2+cos(x))
- (x-pi/3)^2/(-1/2+cos(x))
- 1/(2+cosx)
Limit of the function 1/(2+cos(x))
The solution
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1 lim ---------- x->oo2 + cos(x)
$$\lim_{x \to \infty} \frac{1}{\cos{\left(x \right)} + 2}$$
Limit(1/(2 + cos(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
$$\lim_{x \to \infty} \frac{1}{\cos{\left(x \right)} + 2} = \left\langle \frac{1}{3}, 1\right\rangle$$
$$\lim_{x \to 0^-} \frac{1}{\cos{\left(x \right)} + 2} = \frac{1}{3}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{\cos{\left(x \right)} + 2} = \frac{1}{3}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{\cos{\left(x \right)} + 2} = \frac{1}{\cos{\left(1 \right)} + 2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{\cos{\left(x \right)} + 2} = \frac{1}{\cos{\left(1 \right)} + 2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{\cos{\left(x \right)} + 2} = \left\langle \frac{1}{3}, 1\right\rangle$$
More at x→-oo
$$\lim_{x \to 0^-} \frac{1}{\cos{\left(x \right)} + 2} = \frac{1}{3}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{\cos{\left(x \right)} + 2} = \frac{1}{3}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{\cos{\left(x \right)} + 2} = \frac{1}{\cos{\left(1 \right)} + 2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{\cos{\left(x \right)} + 2} = \frac{1}{\cos{\left(1 \right)} + 2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{\cos{\left(x \right)} + 2} = \left\langle \frac{1}{3}, 1\right\rangle$$
More at x→-oo
The graph