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 -5+x^2+7*x-5*x^3/2
-
Limit of -x+(1+x)/x
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Limit of x^(-x)*(1+x)^x/3
- Graphing y =:
- x/10
- Derivative of:
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x/10
-
Identical expressions
- x/ ten
- x divide by 10
- x divide by ten
-
Similar expressions
- tan(5*x)/(10*x)
- (4+x^2+4*x)/(10+x^2+7*x)
- log(1+5*x)/(10*x)
- (8+x^2-6*x)/(10+x^2-7*x)
- asin(-5+x)/(10+x^2-7*x)
Limit of the function x/10
The solution
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[src]
/x \ lim |--| x->oo\10/
$$\lim_{x \to \infty}\left(\frac{x}{10}\right)$$
Limit(x/10, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{x}{10}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{x}{10}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{10 \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{10 \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{1}{10 u}\right)$$
=
$$\frac{1}{0 \cdot 10} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{x}{10}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{x}{10}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{x}{10}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{10 \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{10 \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{1}{10 u}\right)$$
=
$$\frac{1}{0 \cdot 10} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{x}{10}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(\frac{x}{10}\right) = \infty$$
$$\lim_{x \to 0^-}\left(\frac{x}{10}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{10}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x}{10}\right) = \frac{1}{10}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{10}\right) = \frac{1}{10}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{10}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{x}{10}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x}{10}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x}{10}\right) = \frac{1}{10}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x}{10}\right) = \frac{1}{10}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x}{10}\right) = -\infty$$
More at x→-oo
The graph