Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 5^x-cos(x)
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Limit of 6*x
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Limit of x*sin(x)
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Limit of e^x-x
- Graphing y =:
- e^x-x
- Integral of d{x}:
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e^x-x
- Derivative of:
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e^x-x
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Identical expressions
- e^x-x
- e to the power of x minus x
- ex-x
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Similar expressions
- -2+e^x-x
- x*e^x-x*(1+x)
- e^x+x
- e^x-x-e^(-x)-2*x/sin(x)
- (-1+cosh(5*x))/(-1+e^x-x)
Limit of the function e^x-x
The solution
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/ x \ lim \E - x/ x->oo
$$\lim_{x \to \infty}\left(e^{x} - x\right)$$
Limit(E^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
$$\lim_{x \to \infty}\left(e^{x} - x\right) = \infty$$
$$\lim_{x \to 0^-}\left(e^{x} - x\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(e^{x} - x\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(e^{x} - x\right) = -1 + e$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(e^{x} - x\right) = -1 + e$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(e^{x} - x\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(e^{x} - x\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(e^{x} - x\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(e^{x} - x\right) = -1 + e$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(e^{x} - x\right) = -1 + e$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(e^{x} - x\right) = \infty$$
More at x→-oo
The graph