Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (5-4*x+3*x^2)/(1-x+2*x^2)
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Limit of ((1+2*x)/(-1+x))^(4*x)
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Limit of (4+x^2-5*x)/(-16+x^2)
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Limit of sinh(x)/x
- Graphing y =:
- sin(x/2)
- Derivative of:
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sin(x/2)
- Integral of d{x}:
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sin(x/2)
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Identical expressions
- sin(x/ two)
- sinus of (x divide by 2)
- sinus of (x divide by two)
- sinx/2
- sin(x divide by 2)
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Similar expressions
- x*(sin(x)/2+tan(x)/2)
Limit of the function sin(x/2)
The solution
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/x\ lim sin|-| x->oo \2/
$$\lim_{x \to \infty} \sin{\left(\frac{x}{2} \right)}$$
Limit(sin(x/2), 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
$$\lim_{x \to \infty} \sin{\left(\frac{x}{2} \right)} = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to 0^-} \sin{\left(\frac{x}{2} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sin{\left(\frac{x}{2} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sin{\left(\frac{x}{2} \right)} = \sin{\left(\frac{1}{2} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sin{\left(\frac{x}{2} \right)} = \sin{\left(\frac{1}{2} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sin{\left(\frac{x}{2} \right)} = \left\langle -1, 1\right\rangle$$
More at x→-oo
$$\lim_{x \to 0^-} \sin{\left(\frac{x}{2} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sin{\left(\frac{x}{2} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sin{\left(\frac{x}{2} \right)} = \sin{\left(\frac{1}{2} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sin{\left(\frac{x}{2} \right)} = \sin{\left(\frac{1}{2} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sin{\left(\frac{x}{2} \right)} = \left\langle -1, 1\right\rangle$$
More at x→-oo
The graph