Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-2+2*x^2+log(x))/(e^x-e)
-
Limit of (-x^2+4*x)/(2-sqrt(x))
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Limit of ((2+3*x)/(-1+3*x))^(-1+4*x)
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Limit of (3-x+2*x^2)/(5+x^3-8*x)
- Graphing y =:
- cos(pi*x/2)
- Integral of d{x}:
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cos(pi*x/2)
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Identical expressions
- cos(pi*x/ two)
- co sinus of e of ( Pi multiply by x divide by 2)
- co sinus of e of ( Pi multiply by x divide by two)
- cos(pix/2)
- cospix/2
- cos(pi*x divide by 2)
Limit of the function cos(pi*x/2)
The solution
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/pi*x\ lim cos|----| x->oo \ 2 /
$$\lim_{x \to \infty} \cos{\left(\frac{\pi x}{2} \right)}$$
Limit(cos((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
$$\lim_{x \to \infty} \cos{\left(\frac{\pi x}{2} \right)} = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to 0^-} \cos{\left(\frac{\pi x}{2} \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(\frac{\pi x}{2} \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(\frac{\pi x}{2} \right)} = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(\frac{\pi x}{2} \right)} = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(\frac{\pi x}{2} \right)} = \left\langle -1, 1\right\rangle$$
More at x→-oo
$$\lim_{x \to 0^-} \cos{\left(\frac{\pi x}{2} \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(\frac{\pi x}{2} \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(\frac{\pi x}{2} \right)} = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(\frac{\pi x}{2} \right)} = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(\frac{\pi x}{2} \right)} = \left\langle -1, 1\right\rangle$$
More at x→-oo
The graph