Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (4+x^2)/(-6+2*x)
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Limit of ((1+x)/(1+2*x))^x
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Limit of (n/(1+n))^(5+3*n)
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Limit of (9^x-8^x)/asin(3*x)
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Identical expressions
- ((one +x)/(one + two *x))^x
- ((1 plus x) divide by (1 plus 2 multiply by x)) to the power of x
- ((one plus x) divide by (one plus two multiply by x)) to the power of x
- ((1+x)/(1+2*x))x
- 1+x/1+2*xx
- ((1+x)/(1+2x))^x
- ((1+x)/(1+2x))x
- 1+x/1+2xx
- 1+x/1+2x^x
- ((1+x) divide by (1+2*x))^x
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Similar expressions
- ((1+x)/(1-2*x))^x
- ((1-x)/(1+2*x))^x
Limit of the function ((1+x)/(1+2*x))^x
The solution
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[src]
x
/ 1 + x \
lim |-------|
x->oo\1 + 2*x/
$$\lim_{x \to \infty} \left(\frac{x + 1}{2 x + 1}\right)^{x}$$
Limit(((1 + x)/(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
$$\lim_{x \to \infty} \left(\frac{x + 1}{2 x + 1}\right)^{x} = 0$$
$$\lim_{x \to 0^-} \left(\frac{x + 1}{2 x + 1}\right)^{x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{x + 1}{2 x + 1}\right)^{x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(\frac{x + 1}{2 x + 1}\right)^{x} = \frac{2}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{x + 1}{2 x + 1}\right)^{x} = \frac{2}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{x + 1}{2 x + 1}\right)^{x} = \infty$$
More at x→-oo
$$\lim_{x \to 0^-} \left(\frac{x + 1}{2 x + 1}\right)^{x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{x + 1}{2 x + 1}\right)^{x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(\frac{x + 1}{2 x + 1}\right)^{x} = \frac{2}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{x + 1}{2 x + 1}\right)^{x} = \frac{2}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{x + 1}{2 x + 1}\right)^{x} = \infty$$
More at x→-oo
The graph