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 -1+sqrt(5)-x-2/(sqrt(2)-x)
-
Limit of (-cos(x)^3+cos(x))/(4*x*sin(x))
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Limit of cos((1+x)/x^3)
- Graphing y =:
- x^3/4
- Derivative of:
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x^3/4
- Integral of d{x}:
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x^3/4
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Identical expressions
- x^ three / four
- x cubed divide by 4
- x to the power of three divide by four
- x3/4
- x³/4
- x to the power of 3/4
- x^3 divide by 4
-
Similar expressions
- (-4+x^3)/(4*x^3)
- x^(3/(4+log(3*x)))
Limit of the function x^3/4
The solution
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/ 3\
|x |
lim |--|
x->oo\4 /
$$\lim_{x \to \infty}\left(\frac{x^{3}}{4}\right)$$
Limit(x^3/4, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{x^{3}}{4}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(\frac{x^{3}}{4}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{4 \frac{1}{x^{3}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{4 \frac{1}{x^{3}}} = \lim_{u \to 0^+}\left(\frac{1}{4 u^{3}}\right)$$
=
$$\frac{1}{0 \cdot 4} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{x^{3}}{4}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{x^{3}}{4}\right)$$
Let's divide numerator and denominator by x^3:
$$\lim_{x \to \infty}\left(\frac{x^{3}}{4}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{4 \frac{1}{x^{3}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{4 \frac{1}{x^{3}}} = \lim_{u \to 0^+}\left(\frac{1}{4 u^{3}}\right)$$
=
$$\frac{1}{0 \cdot 4} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{x^{3}}{4}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(\frac{x^{3}}{4}\right) = \infty$$
$$\lim_{x \to 0^-}\left(\frac{x^{3}}{4}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{3}}{4}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{3}}{4}\right) = \frac{1}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{3}}{4}\right) = \frac{1}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{3}}{4}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{x^{3}}{4}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{3}}{4}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{3}}{4}\right) = \frac{1}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{3}}{4}\right) = \frac{1}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{3}}{4}\right) = -\infty$$
More at x→-oo
The graph