Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1-cos(x))/(2*x^2)
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Limit of x^2/(-2+sqrt(4+x^2))
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Limit of (-64+x^2)/(-72+x+x^2)
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Limit of (4-3*x+7*x^4)/(1-2*x+3*x^2)
- Integral of d{x}:
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cos(x)^(-2)
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Identical expressions
- cos(x)^(- two)
- co sinus of e of (x) to the power of ( minus 2)
- co sinus of e of (x) to the power of ( minus two)
- cos(x)(-2)
- cosx-2
- cosx^-2
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Similar expressions
- (1-cos(x^(-2)))*(-3+4*x)
- cos(x)^(2)
- x^4*(1-cos(x^(-2)))
- cosx^(-2)
Limit of the function cos(x)^(-2)
The solution
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[src]
1 lim ------- pi 2 x->--+cos (x) 2
$$\lim_{x \to \frac{\pi}{2}^+} \frac{1}{\cos^{2}{\left(x \right)}}$$
Limit(cos(x)^(-2), x, pi/2)
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
$$\lim_{x \to \frac{\pi}{2}^-} \frac{1}{\cos^{2}{\left(x \right)}} = \infty$$
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+} \frac{1}{\cos^{2}{\left(x \right)}} = \infty$$
$$\lim_{x \to \infty} \frac{1}{\cos^{2}{\left(x \right)}} = \left\langle 0, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-} \frac{1}{\cos^{2}{\left(x \right)}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{\cos^{2}{\left(x \right)}} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{\cos^{2}{\left(x \right)}} = \frac{1}{\cos^{2}{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{\cos^{2}{\left(x \right)}} = \frac{1}{\cos^{2}{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{\cos^{2}{\left(x \right)}} = \left\langle 0, \infty\right\rangle$$
More at x→-oo
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+} \frac{1}{\cos^{2}{\left(x \right)}} = \infty$$
$$\lim_{x \to \infty} \frac{1}{\cos^{2}{\left(x \right)}} = \left\langle 0, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-} \frac{1}{\cos^{2}{\left(x \right)}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{\cos^{2}{\left(x \right)}} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{\cos^{2}{\left(x \right)}} = \frac{1}{\cos^{2}{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{\cos^{2}{\left(x \right)}} = \frac{1}{\cos^{2}{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{\cos^{2}{\left(x \right)}} = \left\langle 0, \infty\right\rangle$$
More at x→-oo
One‐sided limits
[src]
1 lim ------- pi 2 x->--+cos (x) 2
$$\lim_{x \to \frac{\pi}{2}^+} \frac{1}{\cos^{2}{\left(x \right)}}$$
oo
$$\infty$$
= 22801.3333362576
1 lim ------- pi 2 x->---cos (x) 2
$$\lim_{x \to \frac{\pi}{2}^-} \frac{1}{\cos^{2}{\left(x \right)}}$$
oo
$$\infty$$
= 22801.3333362568
= 22801.3333362568
The graph