Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of ((1+x)/(1+2*x))^x
-
Limit of (n/(1+n))^(5+3*n)
-
Limit of (9^x-8^x)/asin(3*x)
-
Limit of (-4+2*x+8*x^2)/(6+4*x)
- Derivative of:
-
3*x^3
- Graphing y =:
- 3*x^3
- Integral of d{x}:
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3*x^3
-
Identical expressions
- three *x^ three
- 3 multiply by x cubed
- three multiply by x to the power of three
- 3*x3
- 3*x³
- 3*x to the power of 3
- 3x^3
- 3x3
-
Similar expressions
- 1-7*x+2*x^2+3*x^3+x^4/3
- cot(4*x)^3*sin(3*x)^3
- asin(2*x)^3/asin(3*x)^3
- (-5*x+4*x^3)/(1-3*x^3)
Limit of the function 3*x^3
The solution
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/ 3\ lim \3*x / x->oo
$$\lim_{x \to \infty}\left(3 x^{3}\right)$$
Limit(3*x^3, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(3 x^{3}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(3 x^{3}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{3} \frac{1}{x^{3}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{3} \frac{1}{x^{3}}} = \lim_{u \to 0^+}\left(\frac{3}{u^{3}}\right)$$
=
$$\frac{3}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(3 x^{3}\right) = \infty$$
$$\lim_{x \to \infty}\left(3 x^{3}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(3 x^{3}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{3} \frac{1}{x^{3}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{3} \frac{1}{x^{3}}} = \lim_{u \to 0^+}\left(\frac{3}{u^{3}}\right)$$
=
$$\frac{3}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(3 x^{3}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(3 x^{3}\right) = \infty$$
$$\lim_{x \to 0^-}\left(3 x^{3}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(3 x^{3}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(3 x^{3}\right) = 3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(3 x^{3}\right) = 3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(3 x^{3}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(3 x^{3}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(3 x^{3}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(3 x^{3}\right) = 3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(3 x^{3}\right) = 3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(3 x^{3}\right) = -\infty$$
More at x→-oo
The graph