Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of 7*tan(9*x/5)/x
-
Limit of (2+x^2-3*x)/(3+x^2-4*x)
-
Limit of -2+e^x-e^(-x)-sin(x)
-
Limit of (2-7*x+3*x^2)/(2-5*x+2*x^2)
- Factor polynomial:
- x^4-x
- Integral of d{x}:
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x^4-x
- Graphing y =:
- x^4-x
-
Identical expressions
- x^ four -x
- x to the power of 4 minus x
- x to the power of four minus x
- x4-x
- x⁴-x
-
Similar expressions
- (x^5-x)/(1+x^4-x^2+5*x^3)
- 1+x^4-x^3-4*x+2/x^3
- (5*x^2+7*x)/(7+x^4-x^2)
- x^4+x
- (x^4-x^2)/(x^2*log(10))
Limit of the function x^4-x
The solution
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/ 4 \ lim \x - x/ x->oo
$$\lim_{x \to \infty}\left(x^{4} - x\right)$$
Limit(x^4 - x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(x^{4} - x\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(x^{4} - x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 - \frac{1}{x^{3}}}{\frac{1}{x^{4}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 - \frac{1}{x^{3}}}{\frac{1}{x^{4}}}\right) = \lim_{u \to 0^+}\left(\frac{1 - u^{3}}{u^{4}}\right)$$
=
$$\frac{1 - 0^{3}}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{4} - x\right) = \infty$$
$$\lim_{x \to \infty}\left(x^{4} - x\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(x^{4} - x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{1 - \frac{1}{x^{3}}}{\frac{1}{x^{4}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{1 - \frac{1}{x^{3}}}{\frac{1}{x^{4}}}\right) = \lim_{u \to 0^+}\left(\frac{1 - u^{3}}{u^{4}}\right)$$
=
$$\frac{1 - 0^{3}}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(x^{4} - x\right) = \infty$$
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
$$\lim_{x \to \infty}\left(x^{4} - x\right) = \infty$$
$$\lim_{x \to 0^-}\left(x^{4} - x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{4} - x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{4} - x\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{4} - x\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{4} - x\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x^{4} - x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x^{4} - x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x^{4} - x\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x^{4} - x\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x^{4} - x\right) = \infty$$
More at x→-oo
The graph