Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (10+12*x)/x^3
- Limit of (1+2*x/3)^(3251035981008077*x/140737488355328)
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Limit of (1-1/(5*n))^(2*n)
- Limit of (10+x)^(1/x)
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Identical expressions
- (ten +x)^(one /x)
- (10 plus x) to the power of (1 divide by x)
- (ten plus x) to the power of (one divide by x)
- (10+x)(1/x)
- 10+x1/x
- 10+x^1/x
- (10+x)^(1 divide by x)
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Similar expressions
- (10-x)^(1/x)
Limit of the function (10+x)^(1/x)
The solution
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[src]
x ________ lim \/ 10 + x x->0+
$$\lim_{x \to 0^+} \left(x + 10\right)^{\frac{1}{x}}$$
Limit((10 + x)^(1/x), x, 0)
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
One‐sided limits
[src]
x ________ lim \/ 10 + x x->0+
$$\lim_{x \to 0^+} \left(x + 10\right)^{\frac{1}{x}}$$
oo
$$\infty$$
= -0.000862230367961205
x ________ lim \/ 10 + x x->0-
$$\lim_{x \to 0^-} \left(x + 10\right)^{\frac{1}{x}}$$
0
$$0$$
= 1.10543492388364e-21
= 1.10543492388364e-21
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \left(x + 10\right)^{\frac{1}{x}} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(x + 10\right)^{\frac{1}{x}} = \infty$$
$$\lim_{x \to \infty} \left(x + 10\right)^{\frac{1}{x}} = 1$$
More at x→oo
$$\lim_{x \to 1^-} \left(x + 10\right)^{\frac{1}{x}} = 11$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(x + 10\right)^{\frac{1}{x}} = 11$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(x + 10\right)^{\frac{1}{x}} = 1$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \left(x + 10\right)^{\frac{1}{x}} = \infty$$
$$\lim_{x \to \infty} \left(x + 10\right)^{\frac{1}{x}} = 1$$
More at x→oo
$$\lim_{x \to 1^-} \left(x + 10\right)^{\frac{1}{x}} = 11$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(x + 10\right)^{\frac{1}{x}} = 11$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(x + 10\right)^{\frac{1}{x}} = 1$$
More at x→-oo