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 (e^x-x-cos(x))/(-x+log(1+x))
-
Limit of (-cos(x)^3+cos(x))/(4*x*sin(x))
- Derivative of:
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-x^4
- Integral of d{x}:
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-x^4
-
Identical expressions
- -x^ four
- minus x to the power of 4
- minus x to the power of four
- -x4
- -x⁴
-
Similar expressions
- (x^5-x^4)/(1-x)
- (x^8-x^7)/(x^5-x^4)
- x^4
- 2-x^2-5*x^3+2*x^5-x^4/3
- (3+x^5-x^4)/(1+x+x^2+x^5)
Limit of the function -x^4
The solution
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/ 4\ lim \-x / x->oo
$$\lim_{x \to \infty}\left(- x^{4}\right)$$
Limit(-x^4, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(- x^{4}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(- x^{4}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{x^{4}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{x^{4}}} = \lim_{u \to 0^+}\left(- \frac{1}{u^{4}}\right)$$
=
$$- \frac{1}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- x^{4}\right) = -\infty$$
$$\lim_{x \to \infty}\left(- x^{4}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(- x^{4}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{x^{4}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\left(-1\right) \frac{1}{x^{4}}} = \lim_{u \to 0^+}\left(- \frac{1}{u^{4}}\right)$$
=
$$- \frac{1}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(- x^{4}\right) = -\infty$$
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
$$\lim_{x \to \infty}\left(- x^{4}\right) = -\infty$$
$$\lim_{x \to 0^-}\left(- x^{4}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{4}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x^{4}\right) = -1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{4}\right) = -1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x^{4}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- x^{4}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{4}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x^{4}\right) = -1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{4}\right) = -1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x^{4}\right) = -\infty$$
More at x→-oo
The graph