Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-16+x^2-6*x)/(-2+x+x^2)
-
Limit of -1+sqrt(5)-x-2/(sqrt(2)-x)
-
Limit of (e^x-x-cos(x))/(-x+log(1+x))
-
Limit of (-cos(x)^3+cos(x))/(4*x*sin(x))
- Integral of d{x}:
-
e-x
- Graphing y =:
- e-x
- Derivative of:
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e-x
-
Identical expressions
- e-x
- e minus x
-
Similar expressions
- e+x
- 1+e^(-x)*(-1+x+x^2)
- 2*x*e^(-x^2)
- x+e^(-x)*x^2
- (-3*e^(4*x)-2*e^(-x)+5*e^(2*x))/(-4*sqrt(1+5*x)+4*cos(3*x)+5*sin(2*x))
- 1-e^(-x)
Limit of the function e-x
The solution
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lim (E - x) x->oo
$$\lim_{x \to \infty}\left(e - x\right)$$
Limit(E - x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(e - x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(e - x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{e}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{e}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{e u - 1}{u}\right)$$
=
$$\frac{-1 + 0 e}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(e - x\right) = -\infty$$
$$\lim_{x \to \infty}\left(e - x\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(e - x\right)$$ =
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{e}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{-1 + \frac{e}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{e u - 1}{u}\right)$$
=
$$\frac{-1 + 0 e}{0} = -\infty$$
The final answer:
$$\lim_{x \to \infty}\left(e - x\right) = -\infty$$
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
$$\lim_{x \to \infty}\left(e - x\right) = -\infty$$
$$\lim_{x \to 0^-}\left(e - x\right) = e$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(e - x\right) = e$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(e - x\right) = -1 + e$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(e - x\right) = -1 + e$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(e - x\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(e - x\right) = e$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(e - x\right) = e$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(e - x\right) = -1 + e$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(e - x\right) = -1 + e$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(e - x\right) = \infty$$
More at x→-oo
The graph