Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (2+2*n)/(2*n)
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Limit of x^5+(1+x)^3-(1+3*x)/x
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Limit of (1-sqrt(x))/(1-x)
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Limit of (1+(1/2)^x)^x
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Identical expressions
- (one +(one / two)^x)^x
- (1 plus (1 divide by 2) to the power of x) to the power of x
- (one plus (one divide by two) to the power of x) to the power of x
- (1+(1/2)x)x
- 1+1/2xx
- 1+1/2^x^x
- (1+(1 divide by 2)^x)^x
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Similar expressions
- (1-(1/2)^x)^x
Limit of the function (1+(1/2)^x)^x
The solution
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[src]
x
/ -x\
lim \1 + 2 /
x->oo
$$\lim_{x \to \infty} \left(1 + \left(\frac{1}{2}\right)^{x}\right)^{x}$$
Limit((1 + (1/2)^x)^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
$$\lim_{x \to \infty} \left(1 + \left(\frac{1}{2}\right)^{x}\right)^{x} = 1$$
$$\lim_{x \to 0^-} \left(1 + \left(\frac{1}{2}\right)^{x}\right)^{x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(1 + \left(\frac{1}{2}\right)^{x}\right)^{x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(1 + \left(\frac{1}{2}\right)^{x}\right)^{x} = \frac{3}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(1 + \left(\frac{1}{2}\right)^{x}\right)^{x} = \frac{3}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(1 + \left(\frac{1}{2}\right)^{x}\right)^{x} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \left(1 + \left(\frac{1}{2}\right)^{x}\right)^{x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(1 + \left(\frac{1}{2}\right)^{x}\right)^{x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(1 + \left(\frac{1}{2}\right)^{x}\right)^{x} = \frac{3}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(1 + \left(\frac{1}{2}\right)^{x}\right)^{x} = \frac{3}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(1 + \left(\frac{1}{2}\right)^{x}\right)^{x} = 0$$
More at x→-oo
The graph