Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of sin(3)^2/x
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Limit of x^4+2*cos(x)^2
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Limit of x*2^x*3^(-x)
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Limit of log(1+3*x^2)/(x^3-5*x^2)
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Identical expressions
- x* two ^x* three ^(-x)
- x multiply by 2 to the power of x multiply by 3 to the power of ( minus x)
- x multiply by two to the power of x multiply by three to the power of ( minus x)
- x*2x*3(-x)
- x*2x*3-x
- x2^x3^(-x)
- x2x3(-x)
- x2x3-x
- x2^x3^-x
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Similar expressions
- x*2^x*3^(x)
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What you mean?
- x*2^x/3^x
- x*2^((x*3)^(-x))
- x*2^((x*3)^(-x))
You entered:
x*2^x*3^(-x)
What you mean?
Limit of the function x*2^x*3^(-x)
The solution
You have entered
[src]
/ x -x\ lim \x*2 *3 / x->oo
$$\lim_{x \to \infty}\left(2^{x} 3^{- x} x\right)$$
Limit(x*2^x/3^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
$$\lim_{x \to \infty}\left(2^{x} 3^{- x} x\right) = 0$$
$$\lim_{x \to 0^-}\left(2^{x} 3^{- x} x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(2^{x} 3^{- x} x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(2^{x} 3^{- x} x\right) = \frac{2}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(2^{x} 3^{- x} x\right) = \frac{2}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(2^{x} 3^{- x} x\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(2^{x} 3^{- x} x\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(2^{x} 3^{- x} x\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(2^{x} 3^{- x} x\right) = \frac{2}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(2^{x} 3^{- x} x\right) = \frac{2}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(2^{x} 3^{- x} x\right) = -\infty$$
More at x→-oo
The graph