Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-2+2*x^2+log(x))/(e^x-e)
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Limit of (-x^2+4*x)/(2-sqrt(x))
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Limit of ((2+3*x)/(-1+3*x))^(-1+4*x)
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Limit of (3-x+2*x^2)/(5+x^3-8*x)
- sin(x/y)
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Identical expressions
- sin(x/y)
- sinus of (x divide by y)
- sinx/y
- sin(x divide by y)
Limit of the function sin(x/y)
The solution
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/x\ lim sin|-| y->oo \y/
$$\lim_{y \to \infty} \sin{\left(\frac{x}{y} \right)}$$
Limit(sin(x/y), y, 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
Other limits y→0, -oo, +oo, 1
$$\lim_{y \to \infty} \sin{\left(\frac{x}{y} \right)} = 0$$
$$\lim_{y \to 0^-} \sin{\left(\frac{x}{y} \right)} = \tilde{\infty} x \cos{\left(\tilde{\infty} x \right)}$$
More at y→0 from the left
$$\lim_{y \to 0^+} \sin{\left(\frac{x}{y} \right)} = \sin{\left(\tilde{\infty} x \right)}$$
More at y→0 from the right
$$\lim_{y \to 1^-} \sin{\left(\frac{x}{y} \right)} = \sin{\left(x \right)}$$
More at y→1 from the left
$$\lim_{y \to 1^+} \sin{\left(\frac{x}{y} \right)} = \sin{\left(x \right)}$$
More at y→1 from the right
$$\lim_{y \to -\infty} \sin{\left(\frac{x}{y} \right)} = 0$$
More at y→-oo
$$\lim_{y \to 0^-} \sin{\left(\frac{x}{y} \right)} = \tilde{\infty} x \cos{\left(\tilde{\infty} x \right)}$$
More at y→0 from the left
$$\lim_{y \to 0^+} \sin{\left(\frac{x}{y} \right)} = \sin{\left(\tilde{\infty} x \right)}$$
More at y→0 from the right
$$\lim_{y \to 1^-} \sin{\left(\frac{x}{y} \right)} = \sin{\left(x \right)}$$
More at y→1 from the left
$$\lim_{y \to 1^+} \sin{\left(\frac{x}{y} \right)} = \sin{\left(x \right)}$$
More at y→1 from the right
$$\lim_{y \to -\infty} \sin{\left(\frac{x}{y} \right)} = 0$$
More at y→-oo