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