Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of x^2*(1/3-cos(8*x)/3)
-
Limit of (-2+x^2-x)/(-2+x+3*x^2)
-
Limit of (-1+sin(x))/cos(x)
-
Limit of (-2*sin(x)+sin(2*x))/(x*log(cos(5*x)))
- Graphing y =:
- x^3-x^4
- Factor polynomial:
- x^3-x^4
- x^3-x^4
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Identical expressions
- x^ three -x^ four
- x cubed minus x to the power of 4
- x to the power of three minus x to the power of four
- x3-x4
- x³-x⁴
- x to the power of 3-x to the power of 4
-
Similar expressions
- x^3+x^4
Limit of the function x^3-x^4
The solution
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/ 3 4\ lim \x - x / x->oo
$$\lim_{x \to \infty}\left(- x^{4} + x^{3}\right)$$
Limit(x^3 - x^4, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(- x^{4} + x^{3}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(- x^{4} + x^{3}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{1}{x}}{\frac{1}{x^{4}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{1}{x}}{\frac{1}{x^{4}}}\right) = \lim_{u \to 0^+}\left(\frac{u - 1}{u^{4}}\right)$$
=
$$\frac{-1}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- x^{4} + x^{3}\right) = -\infty$$
$$\lim_{x \to \infty}\left(- x^{4} + x^{3}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(- x^{4} + x^{3}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{1}{x}}{\frac{1}{x^{4}}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{1}{x}}{\frac{1}{x^{4}}}\right) = \lim_{u \to 0^+}\left(\frac{u - 1}{u^{4}}\right)$$
=
$$\frac{-1}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- x^{4} + x^{3}\right) = -\infty$$
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
$$\lim_{x \to \infty}\left(- x^{4} + x^{3}\right) = -\infty$$
$$\lim_{x \to 0^-}\left(- x^{4} + x^{3}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{4} + x^{3}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x^{4} + x^{3}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{4} + x^{3}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x^{4} + x^{3}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- x^{4} + x^{3}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{4} + x^{3}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x^{4} + x^{3}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{4} + x^{3}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x^{4} + x^{3}\right) = -\infty$$
More at x→-oo
The graph