Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((3+x)^2+(3-x)^2)/((3-x)^2-(3+x)^2)
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Limit of (-1+x)/(-2+sqrt(3+x))
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Limit of (-x+tan(x))/x^3
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Limit of (-1+sqrt(x))/(-3+x)
- Graphing y =:
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x^7
- Derivative of:
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x^7
- Integral of d{x}:
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x^7
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Identical expressions
- x^ seven
- x to the power of 7
- x to the power of seven
- x7
- x⁷
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Similar expressions
- x^7+4/x^2
- log(x)/x^(7/3)
- (x^8-x^7)/(x^5-x^4)
- (1+2/x)^(7*x)
Limit of the function x^7
The solution
Detail solution
Let's take the limit
$$\lim_{x \to \infty} x^{7}$$
Let's divide numerator and denominator by x^7:
$$\lim_{x \to \infty} x^{7}$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{x^{7}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{x^{7}}} = \lim_{u \to 0^+} \frac{1}{u^{7}}$$
=
$$\frac{1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty} x^{7} = \infty$$
$$\lim_{x \to \infty} x^{7}$$
Let's divide numerator and denominator by x^7:
$$\lim_{x \to \infty} x^{7}$$ =
$$\lim_{x \to \infty} \frac{1}{\frac{1}{x^{7}}}$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty} \frac{1}{\frac{1}{x^{7}}} = \lim_{u \to 0^+} \frac{1}{u^{7}}$$
=
$$\frac{1}{0} = \infty$$
The final answer:
$$\lim_{x \to \infty} x^{7} = \infty$$
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
$$\lim_{x \to \infty} x^{7} = \infty$$
$$\lim_{x \to 0^-} x^{7} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} x^{7} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} x^{7} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x^{7} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} x^{7} = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-} x^{7} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} x^{7} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} x^{7} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x^{7} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} x^{7} = -\infty$$
More at x→-oo
The graph