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