Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of sin(2*x)/(5*x)
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Limit of ((3+2*x)/(7+5*x))^(1+x)
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Limit of ((-5+2*x)/(3+2*x))^(7*x)
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Limit of (-6+x+x^2)/(3+x)
- Integral of d{x}:
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sin(x^2)
- Derivative of:
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sin(x^2)
- Graphing y =:
- sin(x^2)
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Identical expressions
- sin(x^ two)
- sinus of (x squared )
- sinus of (x to the power of two)
- sin(x2)
- sinx2
- sin(x²)
- sin(x to the power of 2)
- sinx^2
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Similar expressions
- cos(x)/(1-sin(x))^(2/3)
- 3*sin(x)^2/(4*x)
- sin(x)^2/tan(x^2)
Limit of the function sin(x^2)
The solution
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/ 2\ lim sin\x / x->oo
$$\lim_{x \to \infty} \sin{\left(x^{2} \right)}$$
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
$$\lim_{x \to \infty} \sin{\left(x^{2} \right)} = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to 0^-} \sin{\left(x^{2} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sin{\left(x^{2} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sin{\left(x^{2} \right)} = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sin{\left(x^{2} \right)} = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sin{\left(x^{2} \right)} = \left\langle -1, 1\right\rangle$$
More at x→-oo
$$\lim_{x \to 0^-} \sin{\left(x^{2} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sin{\left(x^{2} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sin{\left(x^{2} \right)} = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sin{\left(x^{2} \right)} = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sin{\left(x^{2} \right)} = \left\langle -1, 1\right\rangle$$
More at x→-oo
The graph