Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of x^(4/x)
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Limit of (-6+x^2-x)/(-4+x^2)
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Limit of (-6+x^2-x)/(-21+x+2*x^2)
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Limit of e^(3-x)*(-2+x)
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Identical expressions
- x^(four /x)
- x to the power of (4 divide by x)
- x to the power of (four divide by x)
- x(4/x)
- x4/x
- x^4/x
- x^(4 divide by x)
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Similar expressions
- (cos(x)^4+sin(x)^4)/x
- (1+x^2+x^4)/(x^2-x+3*x^4)
- sin(x)^4/x^4
- (-3+x^4)/x
- (1+3*x)^(4/x)
Limit of the function x^(4/x)
The solution
You have entered
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4
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x
lim x
x->oo
$$\lim_{x \to \infty} x^{\frac{4}{x}}$$
Limit(x^(4/x), x, oo, dir='-')
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
$$\lim_{x \to \infty} x^{\frac{4}{x}} = 1$$
$$\lim_{x \to 0^-} x^{\frac{4}{x}} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} x^{\frac{4}{x}} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} x^{\frac{4}{x}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x^{\frac{4}{x}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} x^{\frac{4}{x}} = 1$$
More at x→-oo
$$\lim_{x \to 0^-} x^{\frac{4}{x}} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} x^{\frac{4}{x}} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} x^{\frac{4}{x}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x^{\frac{4}{x}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} x^{\frac{4}{x}} = 1$$
More at x→-oo
The graph