Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+1/x)^(-1+x)
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Limit of 7+x^2-14*x/3
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Limit of ((3+x^2-2*x)/(2+x^2-3*x))^(sin(x)/x)
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Limit of (asin(x)^2-atan(x)^2+sin(2*x))/(3*x)
- Graphing y =:
- (2-cos(x))^(x^2)
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Identical expressions
- (two -cos(x))^(x^ two)
- (2 minus co sinus of e of (x)) to the power of (x squared )
- (two minus co sinus of e of (x)) to the power of (x to the power of two)
- (2-cos(x))(x2)
- 2-cosxx2
- (2-cos(x))^(x²)
- (2-cos(x)) to the power of (x to the power of 2)
- 2-cosx^x^2
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Similar expressions
- (2+cos(x))^(x^2)
- (2-cosx)^(x^2)
Limit of the function (2-cos(x))^(x^2)
The solution
You have entered
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\x /
lim (2 - cos(x))
x->0+
$$\lim_{x \to 0^+} \left(2 - \cos{\left(x \right)}\right)^{x^{2}}$$
Limit((2 - cos(x))^(x^2), x, 0)
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]
/ 2\
\x /
lim (2 - cos(x))
x->0+
$$\lim_{x \to 0^+} \left(2 - \cos{\left(x \right)}\right)^{x^{2}}$$
1
$$1$$
= 1.0
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\x /
lim (2 - cos(x))
x->0-
$$\lim_{x \to 0^-} \left(2 - \cos{\left(x \right)}\right)^{x^{2}}$$
1
$$1$$
= 1.0
= 1.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \left(2 - \cos{\left(x \right)}\right)^{x^{2}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(2 - \cos{\left(x \right)}\right)^{x^{2}} = 1$$
$$\lim_{x \to \infty} \left(2 - \cos{\left(x \right)}\right)^{x^{2}} = \left\langle 0, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-} \left(2 - \cos{\left(x \right)}\right)^{x^{2}} = 2 - \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(2 - \cos{\left(x \right)}\right)^{x^{2}} = 2 - \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(2 - \cos{\left(x \right)}\right)^{x^{2}} = \left\langle 0, \infty\right\rangle$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \left(2 - \cos{\left(x \right)}\right)^{x^{2}} = 1$$
$$\lim_{x \to \infty} \left(2 - \cos{\left(x \right)}\right)^{x^{2}} = \left\langle 0, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-} \left(2 - \cos{\left(x \right)}\right)^{x^{2}} = 2 - \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(2 - \cos{\left(x \right)}\right)^{x^{2}} = 2 - \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(2 - \cos{\left(x \right)}\right)^{x^{2}} = \left\langle 0, \infty\right\rangle$$
More at x→-oo
The graph