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