Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-1+e^(2*x))/(3*x)
-
Limit of (-1+3*x)/(5+x^2+7*x)
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Limit of 1+13*x/5
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Limit of (7+x+x^2)/(-1+e^x)
- Derivative of:
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4*x^3
- Integral of d{x}:
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4*x^3
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Identical expressions
- four *x^ three
- 4 multiply by x cubed
- four multiply by x to the power of three
- 4*x3
- 4*x³
- 4*x to the power of 3
- 4x^3
- 4x3
-
Similar expressions
- (1+2*x+2*x^2)/(2-x+4*x^3)
- (-5*x+4*x^3)/(1-3*x^3)
- (1-6*x^3)^(1/(4*x^3))
- cot(4*x)^3*sin(3*x)^3
- (x+4*x^3)/(3-x+2*x^2)
Limit of the function 4*x^3
The solution
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/ 3\ lim \4*x / x->-oo
$$\lim_{x \to -\infty}\left(4 x^{3}\right)$$
Limit(4*x^3, x, -oo)
Detail solution
Let's take the limit
$$\lim_{x \to -\infty}\left(4 x^{3}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to -\infty}\left(4 x^{3}\right)$$ =
$$\lim_{x \to -\infty} \frac{1}{\frac{1}{4} \frac{1}{x^{3}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to -\infty} \frac{1}{\frac{1}{4} \frac{1}{x^{3}}} = \lim_{u \to 0^+}\left(\frac{4}{u^{3}}\right)$$
=
$$\frac{4}{0} = -\infty$$
The final answer:
$$\lim_{x \to -\infty}\left(4 x^{3}\right) = -\infty$$
$$\lim_{x \to -\infty}\left(4 x^{3}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to -\infty}\left(4 x^{3}\right)$$ =
$$\lim_{x \to -\infty} \frac{1}{\frac{1}{4} \frac{1}{x^{3}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to -\infty} \frac{1}{\frac{1}{4} \frac{1}{x^{3}}} = \lim_{u \to 0^+}\left(\frac{4}{u^{3}}\right)$$
=
$$\frac{4}{0} = -\infty$$
The final answer:
$$\lim_{x \to -\infty}\left(4 x^{3}\right) = -\infty$$
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
$$\lim_{x \to -\infty}\left(4 x^{3}\right) = -\infty$$
$$\lim_{x \to \infty}\left(4 x^{3}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(4 x^{3}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(4 x^{3}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(4 x^{3}\right) = 4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(4 x^{3}\right) = 4$$
More at x→1 from the right
$$\lim_{x \to \infty}\left(4 x^{3}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(4 x^{3}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(4 x^{3}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(4 x^{3}\right) = 4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(4 x^{3}\right) = 4$$
More at x→1 from the right
The graph