Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (1-x)^(1/x)
- Limit of (e^(a*x)-e^(b*x))/sin(x)
-
Limit of ((-1+5*x^2)/(-1+7*x^2))^(1+5*x)
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Limit of 5*x^4
- Graphing y =:
- 5*x^4
- 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 multiply by x to the power of 4
- five multiply by x to the power of four
- 5*x4
- 5*x⁴
- 5x^4
- 5x4
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Similar expressions
- 1+2*x+5*x^4+7*x^3+8*x^2/3
- (-8*x^4+4*x^3)/(2+5*x^4)
- (8-x+5*x^4)/(3+x^4)
- (1-x^2+5*x^4)/(3+x^4)
Limit of the function 5*x^4
The solution
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/ 4\ lim \5*x / x->oo
$$\lim_{x \to \infty}\left(5 x^{4}\right)$$
Limit(5*x^4, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(5 x^{4}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(5 x^{4}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{5} \frac{1}{x^{4}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{5} \frac{1}{x^{4}}} = \lim_{u \to 0^+}\left(\frac{5}{u^{4}}\right)$$
=
$$\frac{5}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(5 x^{4}\right) = \infty$$
$$\lim_{x \to \infty}\left(5 x^{4}\right)$$
Let's divide numerator and denominator by x^4:
$$\lim_{x \to \infty}\left(5 x^{4}\right)$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{5} \frac{1}{x^{4}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{5} \frac{1}{x^{4}}} = \lim_{u \to 0^+}\left(\frac{5}{u^{4}}\right)$$
=
$$\frac{5}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(5 x^{4}\right) = \infty$$
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
$$\lim_{x \to \infty}\left(5 x^{4}\right) = \infty$$
$$\lim_{x \to 0^-}\left(5 x^{4}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(5 x^{4}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(5 x^{4}\right) = 5$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(5 x^{4}\right) = 5$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(5 x^{4}\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(5 x^{4}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(5 x^{4}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(5 x^{4}\right) = 5$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(5 x^{4}\right) = 5$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(5 x^{4}\right) = \infty$$
More at x→-oo
The graph