Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((-2+3*x)/(1+3*x))^(2*x)
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Limit of (x/(1+2*x))^x
- Limit of n2*(5/2+n/2)
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Limit of (1-cos(4*x))/(1-cos(8*x))
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Identical expressions
- n two *(five / two +n/2)
- n2 multiply by (5 divide by 2 plus n divide by 2)
- n two multiply by (five divide by two plus n divide by 2)
- n2(5/2+n/2)
- n25/2+n/2
- n2*(5 divide by 2+n divide by 2)
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Similar expressions
- n2*(5/2-n/2)
Limit of the function n2*(5/2+n/2)
The solution
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[src]
/ /5 n\\ lim |n2*|- + -|| n2->0+\ \2 2//
$$\lim_{n_{2} \to 0^+}\left(n_{2} \left(\frac{n}{2} + \frac{5}{2}\right)\right)$$
Limit(n2*(5/2 + n/2), n2, 0)
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
Other limits n2→0, -oo, +oo, 1
$$\lim_{n_{2} \to 0^-}\left(n_{2} \left(\frac{n}{2} + \frac{5}{2}\right)\right) = 0$$
More at n2→0 from the left
$$\lim_{n_{2} \to 0^+}\left(n_{2} \left(\frac{n}{2} + \frac{5}{2}\right)\right) = 0$$
$$\lim_{n_{2} \to \infty}\left(n_{2} \left(\frac{n}{2} + \frac{5}{2}\right)\right) = \infty \operatorname{sign}{\left(n + 5 \right)}$$
More at n2→oo
$$\lim_{n_{2} \to 1^-}\left(n_{2} \left(\frac{n}{2} + \frac{5}{2}\right)\right) = \frac{n}{2} + \frac{5}{2}$$
More at n2→1 from the left
$$\lim_{n_{2} \to 1^+}\left(n_{2} \left(\frac{n}{2} + \frac{5}{2}\right)\right) = \frac{n}{2} + \frac{5}{2}$$
More at n2→1 from the right
$$\lim_{n_{2} \to -\infty}\left(n_{2} \left(\frac{n}{2} + \frac{5}{2}\right)\right) = - \infty \operatorname{sign}{\left(n + 5 \right)}$$
More at n2→-oo
More at n2→0 from the left
$$\lim_{n_{2} \to 0^+}\left(n_{2} \left(\frac{n}{2} + \frac{5}{2}\right)\right) = 0$$
$$\lim_{n_{2} \to \infty}\left(n_{2} \left(\frac{n}{2} + \frac{5}{2}\right)\right) = \infty \operatorname{sign}{\left(n + 5 \right)}$$
More at n2→oo
$$\lim_{n_{2} \to 1^-}\left(n_{2} \left(\frac{n}{2} + \frac{5}{2}\right)\right) = \frac{n}{2} + \frac{5}{2}$$
More at n2→1 from the left
$$\lim_{n_{2} \to 1^+}\left(n_{2} \left(\frac{n}{2} + \frac{5}{2}\right)\right) = \frac{n}{2} + \frac{5}{2}$$
More at n2→1 from the right
$$\lim_{n_{2} \to -\infty}\left(n_{2} \left(\frac{n}{2} + \frac{5}{2}\right)\right) = - \infty \operatorname{sign}{\left(n + 5 \right)}$$
More at n2→-oo
One‐sided limits
[src]
/ /5 n\\ lim |n2*|- + -|| n2->0+\ \2 2//
$$\lim_{n_{2} \to 0^+}\left(n_{2} \left(\frac{n}{2} + \frac{5}{2}\right)\right)$$
0
$$0$$
/ /5 n\\ lim |n2*|- + -|| n2->0-\ \2 2//
$$\lim_{n_{2} \to 0^-}\left(n_{2} \left(\frac{n}{2} + \frac{5}{2}\right)\right)$$
0
$$0$$
0