Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
- Limit of (12+x^2-7*x)/(12+x^3-4*x-3*x^2)
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Limit of -8+5*x^2+6*x
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Limit of (5+x^2-6*x)/(15+x^2-8*x)
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Limit of (6+x^2+5*x)/(3+x)
- Derivative of:
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x-e^(-x)
- Integral of d{x}:
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x-e^(-x)
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Identical expressions
- x-e^(-x)
- x minus e to the power of ( minus x)
- x-e(-x)
- x-e-x
- x-e^-x
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Similar expressions
- x-e^(x)
- x+e^(-x)
Limit of the function x-e^(-x)
The solution
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/ -x\ lim \x - E / x->-oo
$$\lim_{x \to -\infty}\left(x - e^{- x}\right)$$
Limit(x - E^(-x), x, -oo)
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
$$\lim_{x \to -\infty}\left(x - e^{- x}\right) = -\infty$$
$$\lim_{x \to \infty}\left(x - e^{- x}\right) = \infty$$
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
$$\lim_{x \to 0^-}\left(x - e^{- x}\right) = -1$$
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
The graph