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