Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of (4+2*n^3)/(5+n^2)
-
Limit of (-18+12*x+27*x^3)/(-30+2*x^3+5*x+8*x^2)
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Limit of (1+x^2)^4/x^2
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Limit of (1/x)^(1/sin(pi*x))
- Derivative of:
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11/x
- Graphing y =:
- 11/x
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Identical expressions
- eleven /x
- 11 divide by x
- eleven divide by x
Limit of the function 11/x
The solution
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/11\ lim |--| x->oo\x /
$$\lim_{x \to \infty}\left(\frac{11}{x}\right)$$
Limit(11/x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{11}{x}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{11}{x}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{11 \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{11 \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(11 u\right)$$
=
$$0 \cdot 11 = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{11}{x}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{11}{x}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{11}{x}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{11 \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{11 \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(11 u\right)$$
=
$$0 \cdot 11 = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{11}{x}\right) = 0$$
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
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{11}{x}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{11}{x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{11}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{11}{x}\right) = 11$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{11}{x}\right) = 11$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{11}{x}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{11}{x}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{11}{x}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{11}{x}\right) = 11$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{11}{x}\right) = 11$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{11}{x}\right) = 0$$
More at x→-oo
The graph