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