Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
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Limit of (5+3*x)/(-5+x)
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Limit of (-9+x^2)/(15+x^2-8*x)
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Limit of (-1+x)/log(x)
- Limit of (a+x^2-x*(1+a))/(x^3-a^3)
- Graphing y =:
- cos(x/2)
- Derivative of:
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cos(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 divide by 2)
- co sinus of e of (x divide by two)
- cosx/2
- cos(x divide by 2)
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Similar expressions
- (1-cos(x))/(2*x)
- (1-cos(x))/(2*x^2)
Limit of the function cos(x/2)
The solution
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/x\ lim cos|-| x->-oo \2/
$$\lim_{x \to -\infty} \cos{\left(\frac{x}{2} \right)}$$
Limit(cos(x/2), 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
$$\lim_{x \to -\infty} \cos{\left(\frac{x}{2} \right)} = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to \infty} \cos{\left(\frac{x}{2} \right)} = \left\langle -1, 1\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-} \cos{\left(\frac{x}{2} \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(\frac{x}{2} \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(\frac{x}{2} \right)} = \cos{\left(\frac{1}{2} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(\frac{x}{2} \right)} = \cos{\left(\frac{1}{2} \right)}$$
More at x→1 from the right
$$\lim_{x \to \infty} \cos{\left(\frac{x}{2} \right)} = \left\langle -1, 1\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-} \cos{\left(\frac{x}{2} \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(\frac{x}{2} \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(\frac{x}{2} \right)} = \cos{\left(\frac{1}{2} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(\frac{x}{2} \right)} = \cos{\left(\frac{1}{2} \right)}$$
More at x→1 from the right
The graph