Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1-4*x)^(1/x)
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Limit of (-16+x^2+6*x)/(-2-5*x+3*x^2)
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Limit of (1+x)^(2/3)-(-1+x)^(2/3)
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Limit of 1/3+x/3
- Integral of d{x}:
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exp(-2*x)
- Graphing y =:
- exp(-2*x)
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Identical expressions
- exp(- two *x)
- exponent of ( minus 2 multiply by x)
- exponent of ( minus two multiply by x)
- exp(-2x)
- exp-2x
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Similar expressions
- x^3*exp(-2*x^2)
- x^4*exp(-2*x^2)
- exp(2*x)
Limit of the function exp(-2*x)
The solution
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-2*x lim e x->oo
$$\lim_{x \to \infty} e^{- 2 x}$$
Limit(exp(-2*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
$$\lim_{x \to \infty} e^{- 2 x} = 0$$
$$\lim_{x \to 0^-} e^{- 2 x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} e^{- 2 x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} e^{- 2 x} = e^{-2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} e^{- 2 x} = e^{-2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} e^{- 2 x} = \infty$$
More at x→-oo
$$\lim_{x \to 0^-} e^{- 2 x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} e^{- 2 x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} e^{- 2 x} = e^{-2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} e^{- 2 x} = e^{-2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} e^{- 2 x} = \infty$$
More at x→-oo
The graph