Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of cot(x)/csc(x)
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Limit of cos(n)/n
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Limit of 21
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Limit of x^2
- Sum of series:
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21
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Identical expressions
- twenty-one
- 21
- twenty minus one
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Similar expressions
- (2+n)^2*(1+2*n)/(n^2*(3+2*n))
- 2^(1/x)
- (2^n+3^n)/(2^(1+n)+3^(1+n))
- 2^(-n)*2^(1+n)
- ((-1+5*x^2)/(-1+7*x^2))^(1+5*x)
Limit of the function 21
The solution
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
$$\lim_{x \to 0^-} 21 = 21$$
More at x→0 from the left
$$\lim_{x \to 0^+} 21 = 21$$
$$\lim_{x \to \infty} 21 = 21$$
More at x→oo
$$\lim_{x \to 1^-} 21 = 21$$
More at x→1 from the left
$$\lim_{x \to 1^+} 21 = 21$$
More at x→1 from the right
$$\lim_{x \to -\infty} 21 = 21$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} 21 = 21$$
$$\lim_{x \to \infty} 21 = 21$$
More at x→oo
$$\lim_{x \to 1^-} 21 = 21$$
More at x→1 from the left
$$\lim_{x \to 1^+} 21 = 21$$
More at x→1 from the right
$$\lim_{x \to -\infty} 21 = 21$$
More at x→-oo
One‐sided limits
[src]
lim 21 x->0+
$$\lim_{x \to 0^+} 21$$
21
$$21$$
= 21
lim 21 x->0-
$$\lim_{x \to 0^-} 21$$
21
$$21$$
= 21
= 21
The graph