Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
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Limit of 2+((-1+x)/(3+x))^x
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Limit of (-1+x)/(x+x^2)
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Limit of ((1+x)^4-(-1+x)^4)/((1+x)^4+(-1+x)^4)
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Limit of tan(6*x)/(3*x)
- Derivative of:
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5/x^4
- Integral of d{x}:
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5/x^4
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Identical expressions
- five /x^ four
- 5 divide by x to the power of 4
- five divide by x to the power of four
- 5/x4
- 5/x⁴
- 5 divide by x^4
Limit of the function 5/x^4
The solution
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/5 \
lim |--|
x->oo| 4|
\x /
$$\lim_{x \to \infty}\left(\frac{5}{x^{4}}\right)$$
Limit(5/x^4, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{5}{x^{4}}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(\frac{5}{x^{4}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{5 \frac{1}{x^{4}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{5 \frac{1}{x^{4}}}{1}\right) = \lim_{u \to 0^+}\left(5 u^{4}\right)$$
=
$$5 \cdot 0^{4} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{5}{x^{4}}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{5}{x^{4}}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(\frac{5}{x^{4}}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{5 \frac{1}{x^{4}}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{5 \frac{1}{x^{4}}}{1}\right) = \lim_{u \to 0^+}\left(5 u^{4}\right)$$
=
$$5 \cdot 0^{4} = 0$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{5}{x^{4}}\right) = 0$$
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
$$\lim_{x \to \infty}\left(\frac{5}{x^{4}}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{5}{x^{4}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{5}{x^{4}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{5}{x^{4}}\right) = 5$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{5}{x^{4}}\right) = 5$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{5}{x^{4}}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{5}{x^{4}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{5}{x^{4}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{5}{x^{4}}\right) = 5$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{5}{x^{4}}\right) = 5$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{5}{x^{4}}\right) = 0$$
More at x→-oo
The graph