Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+(1+n)^2)/(1+n^2)
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Limit of cot(2*x)/cot(8*x)
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Limit of tan(1/x)/x
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Limit of cos(pi*x)
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Identical expressions
- tan(one /x)/x
- tangent of (1 divide by x) divide by x
- tangent of (one divide by x) divide by x
- tan1/x/x
- tan(1 divide by x) divide by x
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Similar expressions
- (cot(1/x)+tan(1/x))/x
- (x+atan(1/x))/x
- (pi/2+atan(1/x))/x
Limit of the function tan(1/x)/x
The solution
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/ /1\\
|tan|-||
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lim |------|
x->oo\ x /
$$\lim_{x \to \infty}\left(\frac{\tan{\left(\frac{1}{x} \right)}}{x}\right)$$
Limit(tan(1/x)/x, 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
$$\lim_{x \to \infty}\left(\frac{\tan{\left(\frac{1}{x} \right)}}{x}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{\tan{\left(\frac{1}{x} \right)}}{x}\right)$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\tan{\left(\frac{1}{x} \right)}}{x}\right)$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\tan{\left(\frac{1}{x} \right)}}{x}\right) = \tan{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\tan{\left(\frac{1}{x} \right)}}{x}\right) = \tan{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\tan{\left(\frac{1}{x} \right)}}{x}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{\tan{\left(\frac{1}{x} \right)}}{x}\right)$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\tan{\left(\frac{1}{x} \right)}}{x}\right)$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\tan{\left(\frac{1}{x} \right)}}{x}\right) = \tan{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\tan{\left(\frac{1}{x} \right)}}{x}\right) = \tan{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\tan{\left(\frac{1}{x} \right)}}{x}\right) = 0$$
More at x→-oo
The graph