Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-15+x^2-2*x)/(-15-7*x+2*x^2)
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Limit of (-1+e^(5*x))/sin(2*x)
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Limit of x^2*(-cos(4*x)^3/3+cos(4*x)/3)
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Limit of (-4-8*x+8*x^2)/(3+8*x+9*x^2)
- Derivative of:
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sin(x/2)^2
- Integral of d{x}:
- sin(x/2)^2
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Identical expressions
- sin(x/ two)^ two
- sinus of (x divide by 2) squared
- sinus of (x divide by two) to the power of two
- sin(x/2)2
- sinx/22
- sin(x/2)²
- sin(x/2) to the power of 2
- sinx/2^2
- sin(x divide by 2)^2
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Similar expressions
- (sin(x/2)^2)^(cot(x)^2)
- (1-cos(x))/(2*sin(x/2)^2)
- x^2/sin(x/2)^2
Limit of the function sin(x/2)^2
The solution
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[src]
2/x\ lim sin |-| x->0+ \2/
$$\lim_{x \to 0^+} \sin^{2}{\left(\frac{x}{2} \right)}$$
Limit(sin(x/2)^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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \sin^{2}{\left(\frac{x}{2} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sin^{2}{\left(\frac{x}{2} \right)} = 0$$
$$\lim_{x \to \infty} \sin^{2}{\left(\frac{x}{2} \right)} = \left\langle 0, 1\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-} \sin^{2}{\left(\frac{x}{2} \right)} = \sin^{2}{\left(\frac{1}{2} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sin^{2}{\left(\frac{x}{2} \right)} = \sin^{2}{\left(\frac{1}{2} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sin^{2}{\left(\frac{x}{2} \right)} = \left\langle 0, 1\right\rangle$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \sin^{2}{\left(\frac{x}{2} \right)} = 0$$
$$\lim_{x \to \infty} \sin^{2}{\left(\frac{x}{2} \right)} = \left\langle 0, 1\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-} \sin^{2}{\left(\frac{x}{2} \right)} = \sin^{2}{\left(\frac{1}{2} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sin^{2}{\left(\frac{x}{2} \right)} = \sin^{2}{\left(\frac{1}{2} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sin^{2}{\left(\frac{x}{2} \right)} = \left\langle 0, 1\right\rangle$$
More at x→-oo
One‐sided limits
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2/x\ lim sin |-| x->0+ \2/
$$\lim_{x \to 0^+} \sin^{2}{\left(\frac{x}{2} \right)}$$
0
$$0$$
= 7.62280027892881e-33
2/x\ lim sin |-| x->0- \2/
$$\lim_{x \to 0^-} \sin^{2}{\left(\frac{x}{2} \right)}$$
0
$$0$$
= 7.62280027892881e-33
= 7.62280027892881e-33
The graph