Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of sin(3)^2/x
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Limit of x^4+2*cos(x)^2
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Limit of x*2^x*3^(-x)
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Limit of log(1+3*x^2)/(x^3-5*x^2)
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Identical expressions
- sin(pi*x/ three)
- sinus of ( Pi multiply by x divide by 3)
- sinus of ( Pi multiply by x divide by three)
- sin(pix/3)
- sinpix/3
- sin(pi*x divide by 3)
Limit of the function sin(pi*x/3)
The solution
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/pi*x\ lim sin|----| x->oo \ 3 /
$$\lim_{x \to \infty} \sin{\left(\frac{\pi x}{3} \right)}$$
Limit(sin((pi*x)/3), 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
$$\lim_{x \to \infty} \sin{\left(\frac{\pi x}{3} \right)} = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to 0^-} \sin{\left(\frac{\pi x}{3} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sin{\left(\frac{\pi x}{3} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sin{\left(\frac{\pi x}{3} \right)} = \frac{\sqrt{3}}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sin{\left(\frac{\pi x}{3} \right)} = \frac{\sqrt{3}}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sin{\left(\frac{\pi x}{3} \right)} = \left\langle -1, 1\right\rangle$$
More at x→-oo
$$\lim_{x \to 0^-} \sin{\left(\frac{\pi x}{3} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sin{\left(\frac{\pi x}{3} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sin{\left(\frac{\pi x}{3} \right)} = \frac{\sqrt{3}}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sin{\left(\frac{\pi x}{3} \right)} = \frac{\sqrt{3}}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sin{\left(\frac{\pi x}{3} \right)} = \left\langle -1, 1\right\rangle$$
More at x→-oo
The graph