Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of 2^(-n)*2^(1+n)
- Limit of tan(k*x)/x
-
Limit of (-x+tan(x))/(x+2*sin(x))
-
Limit of asin(5*x)/tan(3*x)
- Graphing y =:
- x^4/4
- Derivative of:
-
x^4/4
- Integral of d{x}:
-
x^4/4
-
Identical expressions
- x^ four / four
- x to the power of 4 divide by 4
- x to the power of four divide by four
- x4/4
- x⁴/4
- x^4 divide by 4
Limit of the function x^4/4
The solution
You have entered
[src]
/ 4\
|x |
lim |--|
x->oo\4 /
$$\lim_{x \to \infty}\left(\frac{x^{4}}{4}\right)$$
Limit(x^4/4, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{x^{4}}{4}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(\frac{x^{4}}{4}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{4 \frac{1}{x^{4}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{4 \frac{1}{x^{4}}} = \lim_{u \to 0^+}\left(\frac{1}{4 u^{4}}\right)$$
=
$$\frac{1}{0 \cdot 4} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{x^{4}}{4}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{x^{4}}{4}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(\frac{x^{4}}{4}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{4 \frac{1}{x^{4}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{4 \frac{1}{x^{4}}} = \lim_{u \to 0^+}\left(\frac{1}{4 u^{4}}\right)$$
=
$$\frac{1}{0 \cdot 4} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{x^{4}}{4}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(\frac{x^{4}}{4}\right) = \infty$$
$$\lim_{x \to 0^-}\left(\frac{x^{4}}{4}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{4}}{4}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{4}}{4}\right) = \frac{1}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{4}}{4}\right) = \frac{1}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{4}}{4}\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{x^{4}}{4}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{4}}{4}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{4}}{4}\right) = \frac{1}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{4}}{4}\right) = \frac{1}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{4}}{4}\right) = \infty$$
More at x→-oo
The graph