Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-6-x+2*x^2)/(-2+x)
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Limit of (sqrt(-1+2*x)-(-2+3*x)^(1/5))/(-1+x)
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Limit of (4+2*n^3)/(5+n^2)
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Limit of (2+4*x)/(-3+2*x)
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Identical expressions
- tan(x/ two)/tan(three *x)
- tangent of (x divide by 2) divide by tangent of (3 multiply by x)
- tangent of (x divide by two) divide by tangent of (three multiply by x)
- tan(x/2)/tan(3x)
- tanx/2/tan3x
- tan(x divide by 2) divide by tan(3*x)
Limit of the function tan(x/2)/tan(3*x)
The solution
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[src]
/ /x\ \
| tan|-| |
| \2/ |
lim |--------|
x->oo\tan(3*x)/
$$\lim_{x \to \infty}\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\tan{\left(3 x \right)}}\right)$$
Limit(tan(x/2)/tan(3*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
Rapid solution
[src]
/ /x\ \
| tan|-| |
| \2/ |
lim |--------|
x->oo\tan(3*x)/
$$\lim_{x \to \infty}\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\tan{\left(3 x \right)}}\right)$$
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\tan{\left(3 x \right)}}\right)$$
$$\lim_{x \to 0^-}\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\tan{\left(3 x \right)}}\right) = \frac{1}{6}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\tan{\left(3 x \right)}}\right) = \frac{1}{6}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\tan{\left(3 x \right)}}\right) = \frac{\tan{\left(\frac{1}{2} \right)}}{\tan{\left(3 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\tan{\left(3 x \right)}}\right) = \frac{\tan{\left(\frac{1}{2} \right)}}{\tan{\left(3 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\tan{\left(3 x \right)}}\right)$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\tan{\left(3 x \right)}}\right) = \frac{1}{6}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\tan{\left(3 x \right)}}\right) = \frac{1}{6}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\tan{\left(3 x \right)}}\right) = \frac{\tan{\left(\frac{1}{2} \right)}}{\tan{\left(3 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\tan{\left(3 x \right)}}\right) = \frac{\tan{\left(\frac{1}{2} \right)}}{\tan{\left(3 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\tan{\left(3 x \right)}}\right)$$
More at x→-oo
The graph