Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of -x+x*(2-x)^2
-
Limit of (-3+2*log((3+x)/x))/x
-
Limit of ((-1+2*n)/(1+2*n))^(1+n)
-
Limit of (15-28*x^5-19*x+16*x^2+19*x^3)/(15-30*x^2-7*x^5+11*x^4+23*x)
- Graphing y =:
- x-x^4
- Factor polynomial:
- x-x^4
- Integral of d{x}:
-
x-x^4
-
Identical expressions
- x-x^ four
- x minus x to the power of 4
- x minus x to the power of four
- x-x4
- x-x⁴
-
Similar expressions
- x-x^4/(2-x^3)
- x+x^4
Limit of the function x-x^4
The solution
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/ 4\ lim \x - x / x->oo
$$\lim_{x \to \infty}\left(- x^{4} + x\right)$$
Limit(x - x^4, 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
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{1}{x^{3}}}{\frac{1}{x^{4}}}\right) = \lim_{u \to 0^+}\left(\frac{u^{3} - 1}{u^{4}}\right)$$
=
$$\frac{-1 + 0^{3}}{0} = -\infty$$
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
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{1}{x^{3}}}{\frac{1}{x^{4}}}\right) = \lim_{u \to 0^+}\left(\frac{u^{3} - 1}{u^{4}}\right)$$
=
$$\frac{-1 + 0^{3}}{0} = -\infty$$
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