Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-16+x^2-6*x)/(-2+x+x^2)
-
Limit of -1+sqrt(5)-x-2/(sqrt(2)-x)
-
Limit of (-cos(x)^3+cos(x))/(4*x*sin(x))
-
Limit of cos((1+x)/x^3)
- Graphing y =:
- x/6
- Derivative of:
-
x/6
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Identical expressions
- x/ six
- x divide by 6
- x divide by six
-
Similar expressions
- sin(4*x)/(6*x)
- sin(7*x)/(6*x)
- (6-x)/(6-sqrt(x))
- sin(2*x)/(6*x)
- (-8-3*x^5+5*x)/(6-2*x^7+9*x)
Limit of the function x/6
The solution
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/x\ lim |-| x->oo\6/
$$\lim_{x \to \infty}\left(\frac{x}{6}\right)$$
Limit(x/6, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{x}{6}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{x}{6}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{6 \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{6 \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{1}{6 u}\right)$$
=
$$\frac{1}{0 \cdot 6} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{x}{6}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{x}{6}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{x}{6}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{6 \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{6 \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{1}{6 u}\right)$$
=
$$\frac{1}{0 \cdot 6} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{x}{6}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(\frac{x}{6}\right) = \infty$$
$$\lim_{x \to 0^-}\left(\frac{x}{6}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{6}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x}{6}\right) = \frac{1}{6}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{6}\right) = \frac{1}{6}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{6}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{x}{6}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{6}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x}{6}\right) = \frac{1}{6}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{6}\right) = \frac{1}{6}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{6}\right) = -\infty$$
More at x→-oo
The graph