Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of tan(8*x)/(5*x)
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Limit of x^6
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Limit of cos(x)^4
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Limit of ((1+2*x)^4-(-1+x)^4)/((1+2*x)^4+(-1+x)^4)
- Graphing y =:
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x^6
- Integral of d{x}:
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x^6
- Derivative of:
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x^6
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Identical expressions
- x^ six
- x to the power of 6
- x to the power of six
- x6
- x⁶
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Similar expressions
- log(3*x)^6/sqrt(x)
- ((5+2*x)/(3+x))^(6*x)
- (1+x^5+x^6)/(x^3+x^4)
- (1+2/x)^(6*x)
- (1+x^6-2*x)/(3+x^5-4*x)
Limit of the function x^6
The solution
Detail solution
Let's take the limit
$$\lim_{x \to \infty} x^{6}$$
Let's divide numerator and denominator by x^6:
$$\lim_{x \to \infty} x^{6}$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{x^{6}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{x^{6}}} = \lim_{u \to 0^+} \frac{1}{u^{6}}$$
=
$$\frac{1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty} x^{6} = \infty$$
$$\lim_{x \to \infty} x^{6}$$
Let's divide numerator and denominator by x^6:
$$\lim_{x \to \infty} x^{6}$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{x^{6}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{x^{6}}} = \lim_{u \to 0^+} \frac{1}{u^{6}}$$
=
$$\frac{1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty} x^{6} = \infty$$
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
$$\lim_{x \to \infty} x^{6} = \infty$$
$$\lim_{x \to 0^-} x^{6} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} x^{6} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} x^{6} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x^{6} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} x^{6} = \infty$$
More at x→-oo
$$\lim_{x \to 0^-} x^{6} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} x^{6} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} x^{6} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x^{6} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} x^{6} = \infty$$
More at x→-oo
The graph