Mister Exam
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How to use it?
- Limit of the function:
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Limit of (4-x^2)/(3-x^2)
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Limit of (-2+x^2-x)/(-2+x+3*x^2)
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Limit of 5-9*x+3*x^2/2
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Limit of (-16+x^2)/(-64+x^3)
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Identical expressions
- tan(pi/(four *x))
- tangent of ( Pi divide by (4 multiply by x))
- tangent of ( Pi divide by (four multiply by x))
- tan(pi/(4x))
- tanpi/4x
- tan(pi divide by (4*x))
Limit of the function tan(pi/(4*x))
The solution
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/ pi\ lim tan|---| x->oo \4*x/
$$\lim_{x \to \infty} \tan{\left(\frac{\pi}{4 x} \right)}$$
Limit(tan(pi/((4*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
$$\lim_{x \to \infty} \tan{\left(\frac{\pi}{4 x} \right)} = 0$$
$$\lim_{x \to 0^-} \tan{\left(\frac{\pi}{4 x} \right)} = \left\langle -\infty, \infty\right\rangle$$
More at x→0 from the left
$$\lim_{x \to 0^+} \tan{\left(\frac{\pi}{4 x} \right)} = \left\langle -\infty, \infty\right\rangle$$
More at x→0 from the right
$$\lim_{x \to 1^-} \tan{\left(\frac{\pi}{4 x} \right)} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \tan{\left(\frac{\pi}{4 x} \right)} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \tan{\left(\frac{\pi}{4 x} \right)} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \tan{\left(\frac{\pi}{4 x} \right)} = \left\langle -\infty, \infty\right\rangle$$
More at x→0 from the left
$$\lim_{x \to 0^+} \tan{\left(\frac{\pi}{4 x} \right)} = \left\langle -\infty, \infty\right\rangle$$
More at x→0 from the right
$$\lim_{x \to 1^-} \tan{\left(\frac{\pi}{4 x} \right)} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \tan{\left(\frac{\pi}{4 x} \right)} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \tan{\left(\frac{\pi}{4 x} \right)} = 0$$
More at x→-oo
The graph