Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of cos(x^2)
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Limit of (-sin(x)+cos(x))^(1/x)
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Limit of (cos(x)/cosh(x))^(1/(x*log(1+x)))
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Limit of (-1+cos(x))*cot(x)
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Identical expressions
- x*(one +x)^x
- x multiply by (1 plus x) to the power of x
- x multiply by (one plus x) to the power of x
- x*(1+x)x
- x*1+xx
- x(1+x)^x
- x(1+x)x
- x1+xx
- x1+x^x
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Similar expressions
- x*(1-x)^x
Limit of the function x*(1+x)^x
The solution
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[src]
/ x\ lim \x*(1 + x) / x->0+
$$\lim_{x \to 0^+}\left(x \left(x + 1\right)^{x}\right)$$
Limit(x*(1 + x)^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
The graph
One‐sided limits
[src]
/ x\ lim \x*(1 + x) / x->0+
$$\lim_{x \to 0^+}\left(x \left(x + 1\right)^{x}\right)$$
0
$$0$$
= 6.11760671093707e-29
/ x\ lim \x*(1 + x) / x->0-
$$\lim_{x \to 0^-}\left(x \left(x + 1\right)^{x}\right)$$
0
$$0$$
= -1.44616789078331e-30
= -1.44616789078331e-30
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(x \left(x + 1\right)^{x}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \left(x + 1\right)^{x}\right) = 0$$
$$\lim_{x \to \infty}\left(x \left(x + 1\right)^{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(x \left(x + 1\right)^{x}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \left(x + 1\right)^{x}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \left(x + 1\right)^{x}\right) = -\infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \left(x + 1\right)^{x}\right) = 0$$
$$\lim_{x \to \infty}\left(x \left(x + 1\right)^{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(x \left(x + 1\right)^{x}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \left(x + 1\right)^{x}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \left(x + 1\right)^{x}\right) = -\infty$$
More at x→-oo
The graph