Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of (1+x)/(2+(-7+x)^(1/3))
-
Limit of (-1+x)*cos(1/(-1+x))
-
Limit of x/(1-(1+x)^(1/3))
-
Limit of tan(7*x)^2/sin(4*x^2)
- Graphing y =:
- 1000*x
-
Identical expressions
- one thousand *x
- 1000 multiply by x
- one thousand multiply by x
- 1000x
-
Similar expressions
- 1000^x/factorial(x)
Limit of the function 1000*x
The solution
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lim (1000*x) x->oo
$$\lim_{x \to \infty}\left(1000 x\right)$$
Limit(1000*x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(1000 x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(1000 x\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{1000} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{1000} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{1000}{u}\right)$$
=
$$\frac{1000}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(1000 x\right) = \infty$$
$$\lim_{x \to \infty}\left(1000 x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(1000 x\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{1000} \frac{1}{x}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{1000} \frac{1}{x}} = \lim_{u \to 0^+}\left(\frac{1000}{u}\right)$$
=
$$\frac{1000}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(1000 x\right) = \infty$$
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
$$\lim_{x \to \infty}\left(1000 x\right) = \infty$$
$$\lim_{x \to 0^-}\left(1000 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(1000 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(1000 x\right) = 1000$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(1000 x\right) = 1000$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(1000 x\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(1000 x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(1000 x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(1000 x\right) = 1000$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(1000 x\right) = 1000$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(1000 x\right) = -\infty$$
More at x→-oo
The graph