Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of sin(2/x)
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Limit of (-1+x)^2/(-1+x^2)
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Limit of x-x^2/3
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Limit of sin(3*x^2)/x^2
- Canonical form:
- x-exp(-x)
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Identical expressions
- x-exp(-x)
- x minus exponent of ( minus x)
- x-exp-x
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Similar expressions
- x+exp(-x)
- x-exp(x)
Limit of the function x-exp(-x)
The solution
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/ -x\ lim \x - e / x->oo
$$\lim_{x \to \infty}\left(x - e^{- x}\right)$$
Limit(x - exp(-x), x, oo, dir='-')
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(x - e^{- x}\right) = \infty$$
$$\lim_{x \to 0^-}\left(x - e^{- x}\right) = -1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x - e^{- x}\right) = -1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x - e^{- x}\right) = \frac{-1 + e}{e}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x - e^{- x}\right) = \frac{-1 + e}{e}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x - e^{- x}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x - e^{- x}\right) = -1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x - e^{- x}\right) = -1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x - e^{- x}\right) = \frac{-1 + e}{e}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x - e^{- x}\right) = \frac{-1 + e}{e}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x - e^{- x}\right) = -\infty$$
More at x→-oo
The graph